Lesson 10 1 Angle Relationships Lesson 10 2

Lesson 10 -1 Angle Relationships Lesson 10 -2 Complementary and Supplementary Angles Lesson 10 -3 Statistics: Display Data in a Circle Graph Lesson 10 -4 Triangles Lesson 10 -5 Problem-Solving Investigation: Use Logical Reasoning Lesson 10 -6 Quadrilaterals Lesson 10 -7 Similar Figures Lesson 10 -8 Polygons and Tessellations Lesson 10 -9 Translations Lesson 10 -10 Reflections

Five-Minute Check (over Chapter 9) Main Idea and Vocabulary California Standards Example 1: Naming Angles Key Concept: Types of Angles Example 2: Classify Angles Example 3: Classify Angles Key Concept: Vertical Angles and Adjacent Angles Example 4: Real-World Example

• Classify angles and identify vertical and adjacent angles. • angle • obtuse angle • degrees • straight angle • vertex • vertical angles • congruent angles • adjacent angles • right angle • acute angle

Standard 6 MG 2. 1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Naming Angles Name the angle to the right. Use the vertex as the middle letter and a point from each side. FGH or HGF Use the vertex only. G Use a number. 2 The angle can be named in four ways: FGH, HGF, G, 2.

Naming Angles Answer: FGH, HGF, G, 2

Which of the following is not a name for the angle below? A. RST B. T C. 3 D. S A. B. C. D. A B C D

Classify Angles Classify the angle as acute, obtuse, right, or straight. Answer: The angle is exactly 180°, so it is a straight angle.

Classify the angle as acute, obtuse, right, or straight. A. acute B. obtuse C. right D. straight 1. 2. 3. 4. A B C D

Classify Angles Classify the angle as acute, obtuse, right, or straight. Answer: The angle is less than 90°, so it is an acute angle.

Classify the angle as acute, obtuse, right, or straight. A. acute B. obtuse C. right D. straight 1. 2. 3. 4. A B C D

Answer: 3 and 5 are vertical angles. 3 and 4 are adjacent angles. 4 and 5 are adjacent angles.

For the figure shown, which of the following is true? A. B. C. D. 1. 2. 3. 4. A B C D

Five-Minute Check (over Chapter 10 -1) Main Idea and Vocabulary California Standards Key Concept: Complementary and Supplementary Angles Example 1: Identify Angles Example 2: Identify Angles Example 3: Find a Missing Angle Measure

• Identify complementary and supplementary angles and find missing angle measures. • complementary angle • supplementary angle

Homework: P. 516 – 517: 4 -11 and 22 – 30 CST: 1 - 5

Definition: An angle has two sides that share a common end point.

Definition: The point where the two sides meet is called the vertex. Vertex

Definition: Angles are measured in degrees. 1 degree is one of 360 equal parts of a circle. Protractor

Definition: Angles are named in 4 different ways. 1. FGH 2. HGF 3. G 4. 2

Right Angle

Acute Angle

Obtuse Angle

Straight Angle

Identify Angles Classify the pair of angles as complementary, supplementary, or neither. 128° + 52° = 180° Answer: The angles are supplementary.

Classify the pair of angles as complementary, supplementary, or neither. A. complementary B. supplementary C. neither D. acute 1. 2. 3. 4. A B C D

Identify Angles Classify the pair of angles as complementary, supplementary, or neither. x and y form a right angle. Answer: So, the angles are complementary.

Classify the pair of angles as complementary, supplementary, or neither. A. complementary B. supplementary C. neither D. not enough information 1. 2. 3. 4. A B C D

Find a Missing Angle Measure ALGEBRA Angles PQS and RQS are supplementary. If m PQS = 56°, find m RQS. Words The sum of the measures of PQS and RQS is 180°. Variable Let x represent the measure of RQS. Equation 56 + x = 180

Angles MNP and KNP are complementary. If m MNP = 23°, find m KNP. A. 22 B. 67 C. 157 D. 337 1. 2. 3. 4. A B C D

Five-Minute Check (over Lesson 10 -2) Main Idea and Vocabulary California Standards Example 1: Display Data in a Circle Graph Example 2: Construct a Circle Graph Example 3: Analyze a Circle Graph Example 4: Analyze a Circle Graph

• Construct and interpret circle graphs. • circle graph

Reinforcement of Standard 5 SDAP 1. 2 Organize and display single-variable data in appropriate graphs and representations (e. g. , histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.

Display Data in a Circle Graph SPORTS In a survey, a group of middle-school students was asked to name their favorite sport. The results are shown in the table. Make a circle graph of the data.

Display Data in a Circle Graph Find the degrees for each part. Round to the nearest whole degree.

Display Data in a Circle Graph Use a compass to draw a circle with a radius marked as shown. Then use a protractor to draw the first angle, in this case 108°. Repeat this step for each section.

Display Data in a Circle Graph Check To draw an accurate circle graph, make sure the sum of the angle measures equals 360°. Label each section of the graph with the category and percent. Give the graph a title. Answer: Student’s Favorite Sports

ICE CREAM In a survey, a group of students was asked to name their favorite flavor of ice cream. The results are shown in the table. Make a circle graph of the data.

A. B. C. D. A. B. C. D. A B C D

Construct a Circle Graph MOVIES Gina has the following types of movies in her DVD collection. Make a circle graph of the data. Find the total number of DVDs: 24 + 15 + 7 or 46.

Construct a Circle Graph Find the ratio that compares each number with the total. Write the ratio as a decimal number rounded to the nearest hundredth.

Construct a Circle Graph Find the number of degrees for each section of the graph. action: 0. 52 ● 360 ≈ 187° comedy: 0. 33 ● 360 ≈ 119° science fiction: 0. 15 ● 360 ≈ 54° Draw the circle graph. Check: After drawing the first two sections, you can measure the last section of the circle graph to verify that the angles have the correct measures.

Construct a Circle Graph Answer:

MARBLES Michael has the following colors of marbles in his marble collection. Make a circle graph of the data.

A. C. B. D. 1. 2. 3. 4. A B C D

Analyze a Circle Graph VOTING The circle graph below shows the percent of voters in a town who are registered with a political party. Which party has the most registered voters? The largest section of the circle is the one representing Democrats. So, the Democratic party has the most registered voters. Answer: Democrats

SPORTS The circle graph below shows the responses of middle school students to the question, “Should teens be allowed to play professional sports? ”. Which response was the greatest? A. yes B. no C. no opinion D. not enough information 1. 2. 3. 4. A B C D

Analyze a Circle Graph VOTING The circle graph below shows the percent of voters in a town who are registered with a political party. If the town has 3, 400 registered Republicans, about how many voters are registered in all? 3, 400 Republicans represents 42% of the registered voters.

Analyze a Circle Graph 3, 400 = 42% of registered voters 3, 400 = 0. 42 x x 8, 095 = x Let x represented the number of registered voters. Divide each side by 0. 42. Simplify. There are 8, 095 registered voters in all. Answer: 8, 095

If 275 students responded yes in the sports survey in example 3 your turn, how many students were surveyed in all? A. 325 B. 415 C. 500 D. 625 A. B. C. D. A B C D

Five-Minute Check (over Lesson 10 -3) Main Idea and Vocabulary California Standards Key Concept: Angles of a Triangle Example 1: Find a Missing Measure Example 2: Standards Example Key Concept: Classify Triangles Using Angles and Sides Example 3: Real-World Example 4: Draw Triangles Example 5: Draw Triangles

• Identify and classify triangles. • triangle • obtuse angle • congruent segments • scalene triangle • acute triangle • isosceles triangle • right triangle • equilateral triangle

Standard 6 MG 2. 2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Standard 6 MG 2. 3 Draw quadrilaterals and triangles from given information about them (e. g. , a quadrilateral having equal sides but no right angles, a right isosceles triangle. )

Find a Missing Measure ALGEBRA Find m A in ΔABC if m A = m B and m C = 80. x + 80 = 180 Write the equation. 2 x + 80 = 180 x + x = 2 x – 80 Subtract 80 from each side. 2 x = 100 Simplify. x = 50 Divide each side by 2. Answer: The measure of m A is 50°.

ALGEBRA Find m M in ΔMNO if m N = 75° and m O = 67. A. 25 75 + 67 + x = 180 B. 38 142 + x = 180 – 142 x = 38 A. C. 52 CHECK: D. 61 75 + 67 + 38 = 180 B. C. D. A B C D

An airplane has wings that are shaped like triangles. What is the missing measure of the angle? A 41 B 31 47 + 112 + x = 180 C 26 159 + x = 180 D 21 – 159 x = 21 CHECK: 47 + 112 + 21 = 180

SEWING A piece of fabric is shaped like a triangle. Find the missing measure. A. 73° 73 + 58 + n = 180 B. 49° C. 58° D. 53° 131 + n = 180 – 131 1. 2. 3. 4. CHECK: A Bn C D – 131 = 49 73 + 58 + 49 = 180

Classify the triangle by its angles and its sides. A. acute B. equilateral C. right, scalene D. obtuse, isosceles 1. 2. 3. 4. A B C D

Draw Triangles DRAWING TRIANGLES Susan has drawn a triangle with three acute angles and three congruent sides. Classify the triangle. The triangle has three congruent sides. All three angles are acute. Answer: So, it is an acute equilateral triangle.

DRAWING TRIANGLES Draw a triangle with one right angle and no congruent sides. Classify the triangle. A. right equilateral B. acute scalene C. right scalene D. acute equilaterla A. B. C. D. A B C D

Draw Triangles DRAWING TRIANGLES Phil has drawn a triangle with two acute angles and two congruent sides. Classify the triangle. Because the triangle has two congruent sides, the triangle is isosceles. The triangle has two acute angles and one obtuse angle. Therefore, the triangle is obtuse. Answer: So, it is an obtuse isosceles triangle.

DRAWING TRIANGLES Draw a triangle with three acute angles and two congruent sides. Classify the triangle. A. right isosceles B. acute equilateral C. right scalene D. acute isosceles A. B. C. D. A B C D

Five-Minute Check (over Lesson 10 -4) Main Idea California Standards Example 1: Use Logical Reasoning

• Solve problems by using logical reasoning.

Standard 6 MR 1. 2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. Standard 6 MG 2. 3 Draw quadrilaterals and triangles from given information about them (e. g. , a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Use Logical Reasoning NUMBER BALL Draw an isosceles triangle. How can you confirm that it is isosceles? Use logical reasoning. Explore Isosceles triangles have two congruent sides. You need to find whether two of the sides are congruent. Plan Select adequate method and measuring tools that will allow you to accurately measure the sides of the triangle. Solve Measure and record the lengths of all three sides of the triangle.

Use Logical Reasoning Check If two (or three) of the sides of the triangle have the same length then the triangle is an isosceles triangle. If none of the sides of the triangle are equal then the triangle is not an isosceles triangle. Sample answer: I measured the sides and found that two (or three) of them have the same length.

Draw a right triangle. How can you confirm that it is a right triangle? A. measure the acute angles B. measure the hypotenuse C. measure the right angle D. measure the legs A. B. C. D. A B C D

Five-Minute Check (over Lesson 10 -5) Main Idea and Vocabulary California Standards Example 1: Classify Quadrilaterals Example 2: Classify Quadrilaterals Key Concept: Angles of a Quadrilateral Example 3: Find a Missing Measure

• Identify and classify quadrilaterals. • quadrilateral • parallelogram • trapezoid • rhombus

Standard 6 MG 2. 3 Draw quadrilaterals and triangles from given information about them (e. g. , a quadrilateral having equal sides but no right angles, a right isosceles triangle. )

Classify Quadrilaterals Classify the quadrilateral using the name that best describes it. Answer: The quadrilateral has 4 right angles and opposite sides are congruent. It is a rectangle.

Classify the quadrilateral using the name that best describes it. A. rectangle B. parallelogram C. trapezoid D. square A. B. C. D. A B C D

Classify Quadrilaterals Classify the quadrilateral using the name that best describes it. Answer: The quadrilateral has one pair of parallel sides. It is a trapezoid.

Classify the quadrilateral using the name that best describes it. A. rectangle B. trapezoid C. parallelogram D. square 1. 2. 3. 4. A B C D

Find a Missing Measure ALGEBRA Find the value of x in the quadrilateral shown. Words The sum of the measures is 360°. Variable Let x represent the missing measure. Equation 60 + 120 + 60 + x = 360

Find a Missing Measure 60 + 120 + 60 + x = 360 240 + x Write the equation. = 360 Simplify. – 240 Subtract 240 from each side. x = 120 Answer: The missing angle measure is 120°.

Find the missing angle measure in the quadrilateral. A. 68° B. 109° C. 134° D. 226° 1. 2. 3. 4. A B C D

Five-Minute Check (over Lesson 10 -6) Main Idea and Vocabulary California Standards Key Concept: Similar Figures Example 1: Identify Similar Figures Example 2: Find Side Measures of Similar Triangles Example 3: Real-World Example

• Determine whether figures are similar and find a missing length in a pair of similar figures. • similar figures • corresponding sides • corresponding angles • indirect measurement

Identify Similar Figures Which rectangle is similar to rectangle FGHI?

Find Side Measures of Similar Triangles If ΔABC ~ ΔDEF, find the length of .

If ΔJKL ~ ΔMNO, find the length of A. 9 in. B. 11. 5 in. C. 13. 5 in. D. 15 in. . 1. 2. 3. 4. A B C D

6 8 6 = n 18 · 18 = 8 · n 108 = 8 n 8 8 13. 5 = n

ARCHITECTURE A rectangular picture window 12 -feet long and 6 -feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be?

Tom has a rectangular garden which has a length of 12 feet and a width of 8 feet. He wishes to start a second garden which is similar to the first and will have a width of 6 feet. Find the length of the new garden. A. 4 ft B. 6 ft C. 9 ft D. 10 ft 1. 2. 3. 4. A B C D

Five-Minute Check (over Lesson 10 -7) Main Idea and Vocabulary California Standards Example 1: Classify Polygons Example 2: Classify Polygons Example 3: Angle Measures of a Polygon Example 4: Real-World Example

• Classify polygons and determine which polygons can form a tessellation. • polygon • nonagon • pentagon • decagon • hexagon • regular polygon • heptagon • tessellation • octagon

Standard 6 MR 2. 2 Apply strategies and results from simpler problems to more complex problems. Standard 6 AF 3. 2 Express in symbolic form simple relationships arising from geometry.

Classify Polygons Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why. Answer: The figure is not a polygon since it has a curved side.

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. A. polygon, regular B. pentagon, not regular C. not a polygon D. can’t tell A. B. C. D. A B C D

Classify Polygons Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why. Answer: This figure has 6 sides which are not all of equal length. It is a hexagon that is not regular.

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. A. polygon, regular B. polygon, not regular C. not a polygon D. can’t tell 1. 2. 3. 4. A B C D

Angle Measures of a Polygon ALGEBRA Find the measure of each angle of a regular heptagon. Round to the nearest tenth of a degree. Draw all of the diagonals from one vertex and count the number of triangles formed.

Angle Measures of a Polygon Find the sum of the measures of the polygon. number of triangles sum of angle measures = formed × 180° in polygon 5 × 180° = 900° Find the measure of each angle of the polygon. Let n represent the measure of one angle in the heptagon. 7 n = 900 There are seven congruent angles. n = 128. 6 Divide each side by 7. Answer: The measure of each angle in a regular heptagon is 128. 6°.

Find the measure of each angle in a regular hexagon. A. 90° B. 104. 2° C. 120° D. 132. 8° 1. 2. 3. 4. A B C D

PATTERNS Ms. Pena is creating a pattern on a wall. She wants to use regular hexagons. Can Ms. Pena make a tessellation with regular hexagons? The measure of each angle in a regular hexagon is 120°. The sum of the measures of the angles where the vertices meet must be 360°. . .

n=3 Since 120° divides evenly into 360°, the regular hexagon can be used. Answer: yes Interactive Lab: Tessellations

QUILTING Emily is making a quilt using fabric pieces shaped as equilateral triangles. Can Emily tessellate the quilt with these fabric pieces? A. yes B. no C. maybe D. not enough information A. B. C. D. A B C D

Five-Minute Check (over Lesson 10 -8) Main Idea and Vocabulary California Standards Example 1: Graph a Translation Example 2: Find Coordinates of a Translation

• Graph translations of polygons on a coordinate plane. • transformation • translation • congruent figures

Preparation for Standard 7 MG 3. 2 Understand use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Graph a Translation Translate ΔABC 5 units left and 1 unit up. Move each vertex of the figure 5 units left and 1 unit up. Label the new vertices A , B , and C. Connect the vertices to draw the triangle. Answer: The coordinates of the vertices of the new figure are A'(– 4, – 1), B'(– 1, 2), and C'(0, – 1). Interactive Lab: Translations

Translate ΔDEF 3 units left and 2 units down. A. B. C. D. A. B. C. D. A B C D

Find Coordinates of a Translation Trapezoid GHIJ has vertices G(– 4, 1), H(– 4, 3), I(– 2, 3), and J(– 1, 1). Find the vertices of trapezoid G H I J after a translation of 5 units right and 3 units down. Then graph the figure and its translated image.

Find Coordinates of a Translation Answer: The coordinates of trapezoid G'H'I'J' are G'(1, – 2), H'(1, 0), I'(3, 0), and J'(4, – 2).

Triangle MNO has vertices M(– 5, – 3), N(– 7, 0), and O(– 2, 3). Find the vertices of triangle M N O after a translation of 6 units right and 3 units up. A. M (– 1, 0), N (1, – 3), O (– 4, – 6) B. M (1, 0), N (– 1, 3), O (4, 6) C. M (0, 1), N (3, – 1), O (6, 4) D. M (1, 2), N (– 3, – 2), O (– 4, 3) 1. 2. 3. 4. A B C D

Five-Minute Check (over Lesson 10 -9) Main Idea and Vocabulary California Standards Example 1: Real-World Example 2: Real-World Example 3: Real-World Example 4: Reflect a Figure Over the x-axis Example 5: Reflect a Figure Over the y-axis

• Identify figures with line symmetry and graph reflections on a coordinate plane. • line symmetry • line of symmetry • reflection • line of reflection

Preparation for Standard 7 MG 3. 2 Understand use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry. Answer: This figure has line symmetry. There are two lines of symmetry.

Determine whether the figure has line symmetry. S A. one line of symmetry B. two lines of symmetry C. three lines of symmetry D. no line of symmetry A. B. C. D. A B C D

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry. Answer: This figure has line symmetry. There is one line of symmetry.

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry. A. one line of symmetry B. two lines of symmetry C. three lines of symmetry D. no line of symmetry 1. 2. 3. 4. A B C D

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry. Answer: This figure does not have line symmetry.

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry. A. one line of symmetry B. two lines of symmetry C. three lines of symmetry D. no line of symmetry 1. 2. 3. 4. A B C D

Reflect a Figure Over the x-axis Quadrilateral QRST has vertices Q(– 1, 1), R(0, 3), S(3, 2), and T(4, 0). Graph the figure and its reflected image over the x-axis. Then find the coordinates of the reflected image.

Reflect a Figure Over the x-axis Plot the vertices and connect to form the quadrilateral QRST. The x-axis is the line of symmetry. So, the distance from each point on quadrilateral QRST to the line of symmetry is the same as the distance from the line of symmetry to quadrilateral Q R S T. Answer: Q (– 1, – 1) R (0, – 3) S (3, – 2) T (4, 0)

Quadrilateral ABCD has vertices A(– 3, 2), B(– 1, 5), C(3, 3), and D(2, 1). Find the coordinates of the reflected image over the x-axis. A. A (– 2, – 3), B (– 5, – 1), C (– 3, 3), D (– 1, 2) B. A (0, 2), B (– 1, 3), C (– 2, 1), D (– 4, 5) C. A (– 3, – 2), B (– 1, – 5), C (3, – 3), D (2, – 1) D. A (1, – 3), B (– 2, 4), C (3, – 2), D (0, 0) A. B. C. D. A B C D

Reflect a Figure Over the y-axis Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, – 2). Graph the figure and its reflected image over the y-axis. Then find the coordinates of the reflected image.

Reflect a Figure Over the y-axis Plot the vertices and connect to form the triangle XYZ. The y-axis is the line of symmetry. So, the distance from each point on triangle XYZ to the line of symmetry is the same as the distance from the line of symmetry to triangle X Y Z. Answer: X (– 1, 2), Y (– 2, 1), Z (– 1, – 2)

Triangle QRS has vertices Q(3, 4), R(1, 0), and S(6, 2). Find the coordinates of the reflected image over the y -axis. A. Q (– 2, 3), R (0, 1), S (– 5, 1) B. Q (3, – 4), R (1, 0), S (6, – 2) C. Q (4, 3), R (0, 1), S (2, 6) D. Q (– 3, 4), R (– 1, 0), S (– 6, 2) A. B. C. D. A B C D

Five-Minute Checks Image Bank Math Tools Tessellations Translations

Lesson 10 -1 (over Chapter 9) Lesson 10 -2 (over Lesson 10 -1) Lesson 10 -3 (over Lesson 10 -2) Lesson 10 -4 (over Lesson 10 -3) Lesson 10 -5 (over Lesson 10 -4) Lesson 10 -6 (over Lesson 10 -5) Lesson 10 -7 (over Lesson 10 -6) Lesson 10 -8 (over Lesson 10 -7) Lesson 10 -9 (over Lesson 10 -8) Lesson 10 -10 (over Lesson 10 -9)

To use the images that are on the following three slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® Power. Point® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation.

(over Chapter 9) There are 12 balls in a hat and 3 are red. What is the probability of drawing a red ball? A. B. C. D. A B C D

(over Chapter 9) Use the Fundamental Counting Principle to find the total number of outcomes when choosing an outfit from 3 pairs of pants, 5 shirts, and 4 jackets. A. 12 B. 60 C. 80 D. 120 1. 2. 3. 4. A B C D

(over Chapter 9) How many ways can 7 books be stacked in a single pile? A. 5, 040 B. 49 C. 10, 080 D. 4, 900 1. 2. 3. 4. A B C D

(over Chapter 9) A coin is tossed 14 times. It lands on heads 8 times and on tails 6 times. What is theoretical probability of landing on tails? What is the experimental probability of the coin landing on tails? A. B. C. D. A B C D

(over Chapter 8) A number cube is rolled and the spinner shown in the image is spun. What is the probability of rolling an even number and spinning an odd number? A. B. C. D. 1. 2. 3. 4. A B C D

(over Lesson 10 -1) Classify the angle as acute, obtuse, right, or straight. A. acute B. obtuse C. right D. straight A. B. C. D. A B C D

(over Lesson 10 -1) Classify the angle as acute, obtuse, right, or straight. A. acute B. obtuse C. right D. straight 1. 2. 3. 4. A B C D

(over Lesson 10 -1) Classify the angle as acute, obtuse, right, or straight. A. acute B. obtuse C. right D. straight 1. 2. 3. 4. A B C D

(over Lesson 10 -1) Find the value of x in the figure. A. 72 B. 78 C. 102 D. 112 A. B. C. D. A B C D

(over Lesson 10 -1) Tell whether the following statement is true or false. A straight angle has a measure of 180°. A. true B. false 1. A 2. B

(over Lesson 10 -1) Which of the angles shown in the diagram are adjacent? A. 1 and 3 B. 2 and 3 C. 2 and 4 D. 3 and 1 1. 2. 3. 4. A B C D

(over Lesson 10 -2) Identify the pair of angles as complementary, supplementary, or neither. A. complementary B. supplementary C. neither 1. A 2. B 3. C

(over Lesson 10 -2) Identify the pair of angles as complementary, supplementary, or neither. A. complementary B. supplementary C. neither 1. A 2. B 3. C

(over Lesson 10 -2) Identify the pair of angles as complementary, supplementary, or neither. A. complementary B. supplementary C. neither 1. A 2. B 3. C

(over Lesson 10 -2) Find the value of x. A. 45 B. 60 C. 90 D. 145 A. B. C. D. A B C D

(over Lesson 10 -2) State whether the following statement is true or false. Angles are complementary if the sum of their measures is 180°. A. true B. false 1. A 2. B

(over Lesson 10 -2) If 1 and 2 are complementary angles, and m 1 is 57°, what is the measure of 2? A. 33° B. 43° C. 57° D. 123° 1. 2. 3. 4. A B C D

(over Lesson 10 -3) Which choice shows a circle graph for the set of data in the table? A. B. C. D. A. B. C. D. A B C D

(over Lesson 10 -3) Using the table, what percent of 7 th graders who play sports are on the track and field team? A. 12. 5% B. 18. 75% C. 31. 25% D. 37. 5% 1. 2. 3. 4. A B C D

(over Lesson 10 -4) Find the missing measure in the triangle. Then classify the triangle as acute, right, or obtuse. A. 127°; acute B. 100°; obtuse C. 90°; right 1. 2. 3. A B C

(over Lesson 10 -4) Find the missing measure in the triangle. Then classify the triangle as acute, right, or obtuse. A. 15°; acute B. 15°; obtuse C. 25°; right 1. 2. 3. A. B. C.

(over Lesson 10 -4) Three sides of a triangle measure 3 centimeters, 4 centimeters, and 5 centimeters. Classify the triangle by its sides. A. acute B. equilateral C. obtuse D. scalene 1. 2. 3. 4. A B C D

(over Lesson 10 -4) Two angles of a triangle measure 25° and 45°. Classify the triangle by its angles. A. acute B. equilateral C. obtuse D. scalene A. B. C. D. A B C D

(over Lesson 10 -4) All three angles of a triangle measure 60°. Can you classify the triangle by its sides? Explain. A. No; it is not possible to classify the triangle by its side as the measurements of the sides are not given. B. No; if all three angles of a triangle are 60°, then all three sides are not congruent, and the triangle cannot be classified. 1. C. D. 2. Yes; if all three angles of a triangle are congruent, then all three sides are congruent, 3. and the triangle is a right triangle. 4. Yes; if all three angles of a triangle are congruent, then all three sides are congruent, and the triangle is equilateral. A B C D

(over Lesson 10 -4) Which of the following triangles could not be classified as isosceles? A. equilateral B. scalene C. acute D. right 1. 2. 3. 4. A B C D

(over Lesson 10 -5) Susan pulls out five socks in a drawer. There is a red sock, blue sock, black sock, white sock, and a gray sock. The first sock she pulls out is not blue. The last sock she pulls out is black. She pulls out the blue sock before she pulls out the red rock. The third sock she pulls out is not white or gray. The first sock she pulls out is either gray or red. What color is the third sock? A. red B. blue C. gray D. white A. B. C. D. A B C D

(over Lesson 10 -5) Jo, Leah, Susan, and Brian are in line. Susan is before Brian, Jo is second, and Brian is not last. Who is last in line? A. Jo B. Leah C. Susan D. Brian 1. 2. 3. 4. A B C D

(over Lesson 10 -5) On a family vacation, the Jacksons drove 995 miles in two days. On the first day they drove 131 more miles than the second day. How many miles did they drive on the first day? A. 432 miles B. 500 miles C. 563 miles D. 864 miles 1. 2. 3. 4. A B C D

(over Lesson 10 -5) Which of the following statement is not true about complementary angles? A. Complementary angles are acute. B. Complementary angles’ sum is 90°. C. Complementary angles’ sum is 180°. D. Complementary angles are not right angles. A. B. C. D. A B C D

(over Lesson 10 -6) Classify the quadrilateral using the name that best describes it. A. square B. rectangle C. rhombus D. trapezoid A. B. C. D. A B C D

(over Lesson 10 -6) Classify the quadrilateral using the name that best describes it. A. square B. rectangle C. rhombus D. trapezoid 1. 2. 3. 4. A B C D

(over Lesson 10 -6) Determine and explain whether the statement is sometimes, always, or never true. A square is a parallelogram. A. B. C. Sometimes; parallelograms are quadrilaterals with opposite sides parallel and all sides are not always equal. Always; parallelograms are quadrilaterals with opposite sides parallel and opposite sides congruent. Never; parallelograms are quadrilaterals with only opposite angles congruent. All sides are not congruent. 1. A 2. B 3. C

(over Lesson 10 -6) Determine and explain whether the statement is sometimes, always, or never true. A rhombus is a square. A. B. C. Sometimes true; a rhombus is a parallelogram with 4 congruent sides. If a rhombus also has 4 right angles, it is a square. Always true; all four sides and angles of a rhombus are equal. Never true; an angle of a rhombus cannot be 90° whereas an angle of a square is always 90°. 1. A 2. B 3. C

(over Lesson 10 -6) Which of the following is not a parallelogram? A. sqaure B. rectangle C. trapezoid D. rhombus 1. 2. 3. 4. A B C D

(over Lesson 10 -7) Find the value of x in the pair of similar figures. A. 6. 7 cm B. 10. 6 cm C. 11. 7 cm D. 43. 9 cm A. B. C. D. A B C D

(over Lesson 10 -7) Caren’s dollhouse furniture is made to scale of real furniture with a ratio of inch to 1 foot. If a dollhouse table is 3. 4 inches wide and 4. 2 inches long, what are the dimensions of the “real” table from which it was modeled? A. 16. 3 ft by 20. 1 ft B. 8. 8 ft by 7. 1 ft C. 8. 5 ft by 10. 5 ft D. 1. 4 ft by 1. 7 ft 1. 2. 3. 4. A B C D

(over Lesson 10 -7) Which statement is true? A. All squares are similar. B. All rectangles are similar. C. All right triangles are similar. D. All acute triangles are similar. 1. 2. 3. 4. A B C D

(over Lesson 10 -8) Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why. A. yes; pentagon; regular B. yes; pentagon; not regular C. No; all angles are not equal. D. No; all sides are not of the same length. A. B. C. D. A B C D

(over Lesson 10 -8) Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why. A. yes; quadrilateral; regular B. yes; quadrilateral; not regular C. No; all angles are not equal. D. No; all sides are not equal. 1. 2. 3. 4. A B C D

(over Lesson 10 -8) Find the measure of an angle in a regular hexagon. Round to the nearest tenth of a degree, if necessary. A. 30 B. 60 C. 120 D. 150 1. 2. 3. 4. A B C D

(over Lesson 10 -8) Find the measure of an angle in a regular 16 -gon. Round to the nearest tenth of a degree, if necessary. A. 22. 5 B. 30 C. 150 D. 157. 5 A. B. C. D. A B C D

(over Lesson 10 -8) What is the perimeter of a 13 -gon with each side 3. 2 inches long? A. 83. 2 in. B. 41. 6 in. C. 16. 2 in. D. 10. 2 in. 1. 2. 3. 4. A B C D

(over Lesson 10 -8) Identify the polygons that are used to create the tessellation. A. square and triangle B. rectangle and trapezoid C. trapezoid and square D. rectangle and triangle 1. 2. 3. 4. A B C D

(over Lesson 10 -9) Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 2 units up. A. A'(2, 0), B'(5, 0), C'(5, 4), D'(2, 4) B. A'(0, 2), B'(3, 2), C'(3, 4), D'(0, 4) C. A'(0, 2), B'(3, 2), C'(3, 6), D'(0, 6) D. A'(2, 0), B'(5, 0), C'(3, 4), D'(0, 4) A. B. C. D. A B C D

(over Lesson 10 -9) Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 3 units down. A. A'(0, – 3), B'(3, – 3), C'(3, 1), D'(0, 1) 1. B. A'(– 3, 0), B'(0, 0), C'(0, 4), D'(– 3, 4) 2. 3. C. A'(0, 3), B'(3, 3), C'(3, 7), D'(0, 7) 4. D. A'(0, – 3), B'(7, 0), C'(7, 4), D'(3, 4) A B C D

(over Lesson 10 -9) Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 4 units right and 3 units up. A. A'(4, 0), B'(7, 0), C'(7, 4), D'(4, 4) B. A'(4, 3), B'(7, 3), C'(7, 7), D'(4, 7) C. A'(0, 3), B'(3, 3), C'(3, 7), D'(0, 7) D. A'(3, 4), B'(6, 4), C'(6, 8), D'(3, 8) 1. 2. 3. 4. A B C D

(over Lesson 10 -9) Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 1 unit left and 4 units down. A. A'(1, 0), B'(4, 0), C'(4, 4), D'(1, 4) B. A'(– 1, 4), B'(2, 4), C'(2, 8), D'(– 1, 8) C. A'(1, – 4), B'(4, – 4), C'(4, 0), D'(1, 0) D. A'(– 1, – 4), B'(2, – 4), C'(2, 0), D'(– 1, 0) A. B. C. D. A B C D

(over Lesson 10 -9) Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 3 units right and 2 units down. A. A'(3, – 2), B'(6, – 2), C'(6, 2), D'(3, 2) 1. B. A'(– 2, 3), B'(1, 3), C'(1, 7), D'(– 2, 7) 2. 3. C. A'(3, 2), B'(6, 2), C'(6, 6), D'(3, 6) 4. D. A'(2, – 3), B'(5, – 3), C'(5, 1), D'(2, 1) A B C D

(over Lesson 10 -9) Triangle XYZ has vertices X(1, 3), Y(2, 5), and Z(2, 0). If X'Y'Z' has vertices X'(3, 4), Y'(4, 6), and Z'(4, 1), describe the translation. A. 2 units left, 1 unit up B. 1 unit left, 2 units up C. 2 units right, 1 unit up D. 1 unit right, 2 units up 1. 2. 3. 4. A B C D

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