To be completed today Go to the Brain

To be completed today : Go to the “Brain Pop” app and search watch the “Angles” video. (If you don’t have earbuds, watch with captions) 2. Take the quiz. It will record your results. 1.

Lines Lesson 1

Parallel and Perpendicular Lines Parallel Symbols Define it in your own words Draw it Describe a realworld example of it Perpendicular

Transversals and Angles �

Transversals and Angles

Example 1 � alternate exterior angles

Got it? 1 �

Missing Angle Measures �

Example 2 �

Got it? 2 Find the measure of angle 4.

Example 3 �

Geometric Proof Lesson 2

Deductive vs. Inductive Reasoning Every time Bill watches his favorite team on TV, the team loses. So, he decides to not watch the team play on TV. In order to play sports, you need to have a B average. Simon has a B average, so he concludes that he can play sports. All triangles have 3 sides and 3 angles. Mariah has a figure with 3 sides and 3 angles so it must be a triangle. After performing a science experiment, La. Dell concluded that only 80% of tomato seeds would grow into plants. Deductive Reasoning Inductive Reasoning

The Proof Process STEP 1: List the given information, or what you know. Draw a diagram if needed. STEP 2: State what is to be proven. STEP 3: Create a deductive argument by forming a logical chain of statements linking the given information. STEP 4: Justify each statement with definitions, properties, and theorems STEP 5: State what it is you have proven.

Vocabulary A proof is a logical argument where each statement is justified by a reason. A paragraph proof or informal proof involves writing a paragraph. A two-column proof or formal proof contains statements and reason organized in two columns. Once a statement has been proven, it is a theorem.

Example 1 – Paragraph Proof �

Got it? 1 Refer to the diagram shown. AR = CR and DR = BR. Write a paragraph proof to show that AR + DR = CR + BR. Given: AR = ______ and DR = ______. Prove: _________ = CR + BR. Proof: You know that AR = CR and DR = BR. AR + DR = CR + BR by the _______ Property of Equality. So, AR + DR = CR + BR by __________.

Example 2 � Reasons Statements Given Definition of linear pair Definition of supplemental angles Substitution Subtraction Property of Equality

Got it? 2 � Reasons Statements Given

Angles of Triangles Lesson 3

Real-World Link �

Angle Sum of a Triangle Words: The sum of the measures of the interior angles of a triangle is 180˚. Symbols: Model: x + y + z = 180˚.

Example 1 Find the value of x in the Antigua and Barbuda flag. x + 55 + 90 = 180 x + 145 = 180 x = 35 The value of x is 35.

Got it? 1 �

Example 2 The measures of the angles of ΔABC are in the ratio 1: 4: 5. What are the measures of the angles? Let x represent angle A, 4 x angle B, and 5 x angle C x + 4 x + 5 x = 180 10 x = 180 x = 18 Angle A = 18˚ Angle B = 18(4) = 72˚ Angle C = 18(5) = 90˚

Got it? 2 The measures of the angles of ΔLMN are in the ratio 2: 4: 6. What are the measures of the angles?

Exterior Angles of a Triangle �

Interior and Exterior Angles Each exterior angle of the triangle has two remote interior angles that are not adjacent to the exterior angle. 4 1 interior exterior 3 5 2 6

Example 3 �

Got it? 3 �

Polygons and Angles Lesson 4

Real-World Link A polygon is a closed figure with three of more line segments. List the states that are in a shape of a polygon.

Interior Angle Sum of a Polygon Words: The sum of the measures of the interior angles of a polygon is (n – 2)180, where n is the number of sides. Symbols: S = (n – 2)180 Regular Polygons – an equilateral (all sides are the same) and a equiangular (all angles are the same)

Interior Angle Sum of a Polygon

Example 1 Find the sum of the measures of the interior angles of a decagon. S = (n -2)180 S = (10 – 2)180 S = (8)180 S = 1, 440 The sum of the interior angles of a 10 -sided polygon is 1, 440˚.

Got it? 1 Find the sum of the measures of the interior angles of each polygon. a. Hexagon b. Octagon c. 15 -gon

Example 2 Each chamber of a bee honeycomb is a regular hexagon. Find the measure of an interior angle of a regular hexagon. STEP 1: Find the sum of the measures of angle. S = (n – 2)180 S = (6 – 2)180 S = (4)180 S = 720˚ STEP 2: Divide 720 by 6, since there are six angles in a hexagon. 720˚÷ 6 = 120 Each angle in a hexagon is 120˚

Got it? 2 Find the measure of one interior angle in each regular polygon. Round to the nearest tenth if necessary. a. octagon b. heptagon c. 20 -gon

Exterior Angles of a Polygon �

Example 3 Find the measure of an exterior angle in a regular hexagon. A hexagon has a 6 exterior angles. 6 x = 360 x = 60 Each exterior angle is 60˚.

Got it? 3 Find the measure of an exterior angle in a regular polygon. a. triangle b. quadrilateral c. octagon

The Pythagorean Theorem Lesson 5

Pythagorean Theorem Words: In a right triangle, the sum of the squares of the legs equal the square of the hypotenuse. Symbols: a 2 + b 2 = c 2 Model: c a b

Example 1 Find the missing length. Round to the nearest tenth. c 12 in 9 in

Example 2 Find the missing length. Round to the nearest tenth. b 24 cm 8 cm

Got it? 1 and 2 Find the missing length. Round to the nearest tenth if necessary. a. b.

Converse of Pythagorean Theorem STATEMENT: If a triangle is a right triangle, then a 2 + b 2 = c 2. CONVERSE: If a 2 + b 2 = c 2, then a triangle is a right triangle. The converse of the Pythagorean Theorem is also true.

Example 3 The measures of three sides of a triangle are 5 inches, 12 inches and 13 inches. Determine whether the triangle is a right triangle. a 2 + b 2 = c 2 52 + 122 = 132 25 + 144 = 169 The triangle is a right triangle.

Got it? 3 Determine if these side lengths makes a right triangle. a. 36 in, 48 in, 60 in b. 4 ft, 7 ft, 5 ft

Use the Pythagorean Theorem Lesson 6

Example 1 Write an equation that can be used to find the length of the ladder. Then solve. Round to the nearest tenth.

Example 2 Write an equation that can be used to find the length of the ladder. Then solve. Round to the nearest tenth.

Got it? 1 & 2 Mr. Parsons wants to build a new banister for the staircase shown. If the rise of the stairs of a building is 5 feet and the run is 12 feet, what will be the length of the new banister?

Example 3 A 12 -foot flagpole is placed in the center of a square area. To stabilize the pole, a wire will stretch from the top of the pole to each corner of the square. The flagpole is 7 feet from each corner of the square. what is the length of each wire. Round to the nearest tenth.

Got it? 3 The top part of a circus tent is in the shape of a cone. The tent has a radius of 50 feet. The distance from the top of the tent to the edge is 61 feet. How tall is the top part of the tent? Round to the nearest whole number.

Distance on the Coordinate Plane Lesson 7

Example 1 Graph the ordered pairs (3, 0) and (7, 5). Then find the distance c between the two points. Round to the nearest tenth.

Got it? 1 Graph the ordered pairs (1, 3) and (-2, 4). Then find the distance c between the two points. Round to the nearest tenth.

The Distance Formula �

Example 2 On the map, each unit represents 45 miles. West Point, New York is located at (1. 5, 2) and Annapolis, Maryland, is located at (-1. 5, -1. 5). What is the approximate distance between West Point and Annapolis? Since the map units equals 45 miles, the distance between the cities is 4. 6(45) or about 207 miles.

Got it? 2 Cromwell Field is located at (2. 5, 3. 5) and Deadwoods Field is at (1. 5, 4. 5) on a map. If each map unit is 0. 1 mile, about how far apart are the fields?

Example 3 �