2019 GEOMETR Y boot camp Congruence Similarity Right

2019 GEOMETR Y boot camp Congruence, Similarity, Right Triangles, and Trigonometry

MAFS. 912. G-CO. 1. 1 Drag the words to the correct descriptions. Not all options will be used. Circle Line the set of points extending in one direction in a plane the set of points between two endpoints in a plane Angle Line Segment Ray the set of all points the same distance from a given point in a plane the set of points extending in opposite directions in a plane

MAFS. 912. G-CO. 1. 1 Classify each statement in the table as correct or incorrect. Select one cell per row. Correct If two lines in the same plane do not intersect, the lines must be parallel. If two line in the space do not intersect, the lines must be parallel. If two lines are parallel, the lines must lie in the same plane. Incorrect

MAFS. 912. G-CO. 1. 1 Refer to the diagram. Which terms are demonstrated in the figure? Select all that apply. q Circle q Angle q Skew lines q Parallel lines q Line segment q Perpendicular lines

MAFS. 912. G-CO. 1. 1 Points A and B are on a line. What is the best definition of line segment AB? A. Points A and B, and points between them B. Points A and B, and all points on side of A C. Points A and B, and all points on the line between them D. Points A and B, and the line containing them

MAFS. 912. G-CO. 1. 1

MAFS. 912. G-CO. 1. 2 Choose the graph that shows the correct placement of A’B’C’D’E’ after the transformation. A B C D

MAFS. 912. G-CO. 1. 2 Which single transformation would carry Figure 1 onto Figure 3? A. a dilation B. a rotation C. a reflection D. a translation

MAFS. 912. G-CO. 1. 2

MAFS. 912. G-CO. 1. 2 The pre-image of △ABC and its image △A′B′C′ are shown on the coordinate plane. Which rule describes the transformation represented in the graph?

MAFS. 912. G-CO. 1. 4 Which statement must be true? Select all that apply.

MAFS. 912. G-CO. 1. 4

MAFS. 912. G-CO. 1. 3 Which figure always has exactly four lines of reflection that map the figure onto itself? A. square B. rectangle C. regular octagon D. equilateral triangle

MAFS. 912. G-CO. 1. 3 Select the values that correctly complete the sentence about the symmetry of a regular pentagon. A regular pentagon has _____ lines of symmetry and 1 2 5 6 has ______ rotational symmetry. 60 degree 72 degree 108 degree 540 degree

MAFS. 912. G-CO. 1. 3 Trapezoid RSTU is shown. Write the equation for the line that would map the trapezoid onto itself.

MAFS. 912. G-CO. 1. 3 Figure 1 is a rhombus and Figure 2 is a rectangle. Neither figure is a square. Which transformation can be used to map Figure 1 onto itself and can also be used to map Figure 2 onto itself?

MAFS. 912. G-CO. 1. 3 The figure below shows a rhombus with noncongruent diagonals. Which transformation would not carry this rhombus onto itself? A. a reflection over the shorter diagonal B. a reflection over the longer diagonal C. a clockwise rotation of 90° about the intersection of the diagonals D. a counterclockwise rotation of 180° about the intersection of the diagonals

MAFS. 912. G-CO. 1. 3 Which transformation would not carry this rectangle onto itself?

MAFS. 912. G-CO. 1. 3 The regular polygon below is rotated about its center. Which angle of rotation will carry the figure onto itself? A. 60° B. 108° C. 216° D. 540°

MAFS. 912. G-CO. 1. 5

MAFS. 912. G-CO. 1. 5 △ABC is shown on the coordinate plane. After rotating △ABC 180° about the origin and then reflecting it over the x-axis, what are the coordinates of △A″B″C″? A. A″(2, 6), B″(5, 4), C″(2, 1) B. A″(6, 2), B″(4, 5), C(1, 2) C. A″(− 2, 6), B″(5, 4), C″(− 2, 1) D. A″(6, − 2), B″(4, − 5), C″(1, − 2)

MAFS. 912. G-CO. 1. 5

MAFS. 912. G-CO. 1. 5 Enter the coordinates for the resulting image A″B″C″D″ in the boxes. A” = B” = C” = D” =

MAFS. 912. G-CO. 1. 5 Triangle EGF is graphed below. Triangle EGF will be rotated 90° counterclockwise around the origin and will then be reflected across the y-axis, producing an image triangle. Which additional transformation will map the image triangle back onto the original triangle?

MAFS. 912. G-CO. 1. 5

MAFS. 912. G-CO. 1. 5 Quadrilateral ABCD is graphed in a coordinate plane.

MAFS. 912. G-CO. 1. 5 (continued from previous slide)

MAFS. 912. G-CO. 1. 5 Triangle ABC and triangle ADE are shown. Select all the transformations that could be performed to carry triangle ABC onto triangle ADE.

MAFS. 912. G-CO. 2. 6 the coordinates of A’ will be the same will not be the same the coordinates of C’

MAFS. 912. G-CO. 2. 6 Which statement must be true?

MAFS. 912. G-CO. 2. 6 Triangle MNO is transformed to produce triangle PQR. Select all the transformations that would guarantee triangles MNO and PQR are congruent. q a dilation, then a translation q a reflection, then a dilation q a reflection, then a rotation q a rotation, then a translation q a translation, then a reflection

MAFS. 912. G-CO. 2. 6 A series of transformations will be performed on a figure that is graphed on a coordinate plane. Which of the following series of transformations would produce a congruent figure? Select all that apply.

MAFS. 912. G-CO. 2. 6 Statement True False

MAFS. 912. G-CO. 2. 6 In the illustration, figure I and figure II are isosceles trapezoids. Tran makes a conjecture that figure I is congruent to figure II. Select each transformation or combination of transformations that can help Tran prove his conjecture. Select all that apply.

MAFS. 912. G-CO. 2. 6

MAFS. 912. G-CO. 2. 7 Select all the statements that must be true.

MAFS. 912. G-CO. 2. 7 △ABC and △DEF are plotted on the coordinate plane shown. q △ABC ≅ △DEF q △ABC ∼△DEF q △ABC is acute, but △DEF is obtuse. q All corresponding sides are congruent.

MAFS. 912. G-CO. 2. 8 Aniyah has repeatedly stenciled the triangle shape shown on her bedroom wall. Her best friend, Daniela, wants to copy the exact same shape on her bedroom wall. Which statement has sufficient information about the triangle for Aniyah to give to Daniela to guarantee Daniela will have the exact same triangle? A. Construct a triangle with angles whose measures are 33°, 42°, and 105°. B. Construct a triangle with sides of measure 22 inches and 27 inches where the included angle is 105°. C. Construct a triangle with sides of measure 39 inches and 22 inches and a nonincluded angle of measure 33°. D. Construct a triangle with a 105° angle opposite from a side of length 39 inches where the remaining two sides differ in length by 5 inches.

MAFS. 912. G-CO. 3. 9 A. 36° B. 42° C. 78° D. 102°

MAFS. 912. G-CO. 3. 9 A. 5 B. 9 C. 14 D. 17

MAFS. 912. G-CO. 3. 9 Which statement is true?

MAFS. 912. G-CO. 3. 9

MAFS. 912. G-CO. 3. 9 Which statements could be used to complete Mikayla’s proof? Statements Reasons A. 1 TP is a line 2 Definition of supplementary angles B. 3 Property of angle bisectors C. 4 Substitution 5 Division property of equality 6 Definition of complementary angles D.

MAFS. 912. G-CO. 3. 9 Select from the drop-down menus to support each line of the proof.

MAFS. 912. G-CO. 3. 9 Statements Reasons Given All right angles are congruent Definition of bisector J is equidistant from L and K Reflexive property of equality Definition of right angle SAS Definition of perpendicular Definition of equidistant Corresponding parts of congruent triangles are congruent

MAFS. 912. G-CO. 3. 9 Part of a proof is shown. Place statements and reasons in the table to complete the proof. Statements Vertical angles theorem Reasons Given Corresponding angles postulate Transitive property Alt. exterior angles theorem Reflexive property Angle addition postulate

MAFS. 912. G-CO. 3. 10 Roads connecting the towns of Oceanside, River City, and Lake View form a triangle. The distance from Oceanside to River City is 38 kilometers. The distance from River City to Lake View is 26 kilometers. What is the smallest possible whole number of kilometers between Lake View and Oceanside? Enter your answer in the box.

MAFS. 912. G-CO. 3. 10 Which of the statements about the figure cannot be proven?

MAFS. 912. G-CO. 3. 10 Which of the following sets of lengths could form the sides of a triangle? Choose all that apply. q 5, 9, 7 q 4, 8, 3 q 11, 22 q 2, 5, 4 q 7, 9, 12 q 10, 8, 2

MAFS. 912. G-CO. 3. 10 Complete the proof by filling in the missing reasons from the “Reasons Bank” below. Reasons Bank AA Similarity Postulate Statements Reasons Given SAS Similarity Theorem SSS Similarity Theorem Vertical angles are congruent If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent. If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent

MAFS. 912. G-CO. 3. 10 Which equation is always true?

MAFS. 912. G-CO. 3. 11 Which statement about parallelograms is always true? A. The diagonals are congruent. B. The diagonals bisect each other. C. The diagonals are perpendicular. D. The diagonals bisect their respective angles.

MAFS. 912. G-CO. 3. 11

MAFS. 912. G-CO. 3. 11 Which set of statements would describe a parallelogram that can always be classified as a rhombus? I. Diagonals are perpendicular bisectors of each other. II. Diagonals bisect the angles from which they are drawn. III. Diagonals form four congruent isosceles right triangles. A. I and II B. I and III C. II and III D. I, II, and III

MAFS. 912. G-CO. 3. 11 A. 5 units B. 10 units C. 19 units D. 38 units

MAFS. 912. G-CO. 3. 11 Parallelogram ABCD is shown. Enter the correct values in the boxes.

MAFS. 912. G-CO. 3. 11 Enter your answer in the box.

MAFS. 912. G-CO. 3. 11 A. 80 units B. 40 units C. 20 units D. 10 units

MAFS. 912. G-CO. 3. 11 Parallelogram ABCD is a _________ because the __________.

MAFS. 912. G-CO. 3. 11 Statements Reasons Given S. S. S Definition of a parallelogram S. A Opposite sides of a parallelogram are congruent Corresponding parts of congruent triangles are congruent Definition of congruent segments When two parallel lines are cut by a transversal, corresponding angles are congruent When two parallel lines are cut by a transversal, same side interior angles are congruent When two parallel lines are cut by a transversal, alternate interior angles are congruent

MAFS. 912. G-CO. 3. 11 Given: ABCD is a parallelogram Proof: Opposite angles of a parallelogram are congruent. Thus _____ and _____ by the _______. Definition of congruence Definition of equality Using the ________, ________. By the ________, ________. Division property of equality Substitution property of equality Transitive property of equality

MAFS. 912. G-CO. 3. 11 Statements Reasons Pythagorean Theorem Substitution Definition of congruent lines Property of a parallelogram PQRS is Definition of a rhombus Pythagorean Theorem Definition of perpendicular lines Property of a parallelogram Definition of parallel lines

MAFS. 912. G-CO. 3. 11 Statements WXYZ is a parallelogram Reasons Pythagorean Theorem Corresponding angles are congruent Alt. exterior angles are congruent Alt. interior angles are congruent C. P. C. T. C. Definition of a parallelogram Transitive property Angle addition postulate Reflexive property Segment addition postulate

MAFS. 912. G-CO. 3. 11 Consider parallelogram ABCD with point X at the intersection of diagonal segments AC and BD. Evelyn claims that ABCD is a square. Select all statements that must be true for Evelyn’s claim to be true.

MAFS. 912. G-CO. 4. 12 Which of the following best describes the construction?

MAFS. 912. G-CO. 4. 12 A student is working on a geometric construction. A. angle bisector B. copying an angle C. perpendicular bisector D. measuring an angle

MAFS. 912. G-CO. 4. 12 The figure above shows the construction of the angle bisector of angle AOB using a compass. Which of the following statements must always be true in the construction of the angle bisector? Classify each statement in the table as correct or incorrect. Select one cell per row. Correct Incorrect

MAFS. 912. G-CO. 4. 12 Part A Consider the partial construction of a line parallel to r through point Q. What would be the final step in the construction? A. B. C. D. draw a a line through P and S Q and S T and S Wand S Part B Once the construction is complete, which of the reasons listed contribute to proving the validity of the construction? A. When two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. B. When two lines are cut by a transversal and the vertical angles are congruent, the lines are parallel. C. definition of segment bisector D. definition of an angle bisector

MAFS. 912. G-CO. 4. 13 What should be Steven’s next step in constructing the equilateral triangle?

MAFS. 912. G-SRT. 1. 1 The diagram represents a dilation with a center at P.

MAFS. 912. G-SRT. 1. 1 Triangle ABC has been dilated from center D. A. 2 x B. 3 x C. 4 x D. 5 x

MAFS. 912. G-SRT. 1. 1 In the figure, point P will be the center of dilation of triangle ABC. Point P is collinear with vertices B and C. The scale factor of the dilation will be 3. Consider the relationship between the sides of triangle ABC and the sides of the dilation image, triangle A’B’C’. Select from the drop-down menus to correctly complete each sentence. Side A’B’ will side AB. Side A’C’ will side AC. Side B’C’ will side BC.

MAFS. 912. G-SRT. 1. 1 The image shown will undergo a dilation centered at point B, with a scale factor of 2. Which lines will not be changed by the transformation?

MAFS. 912. G-SRT. 1. 1 Line segment AB is shown on the coordinate grid. Line segment AB is dilated by a scale factor of 2, with the center of dilation at the origin, resulting in line segment A’B’. Use the Connect Line tool to draw segment A’B’.

MAFS. 912. G-SRT. 1. 1 A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true? A. The line segments are perpendicular, and the image is one-half of the length of the given line segment. B. The line segments are perpendicular, and the image is twice the length of the given line segment. C. The line segments are parallel, and the image is twice the length of the given line segment. D. The line segments are parallel, and the image is one-half of the length of the given line segment.

MAFS. 912. G-SRT. 1. 1

MAFS. 912. G-SRT. 1. 1 Part A: What is the slope of the line after the dilation? Part A Part B

MAFS. 912. G-SRT. 1. 2 Two triangles are shown. Which is a true statement about the two triangles? A. The triangles are not similar. B. △ABC ∼△EDF by AA Similarity Postulate C. △ABC ∼△FDE by SAS Similarity Postulate D. △ABC ∼△FDE by AA Similarity Postulate

MAFS. 912. G-SRT. 1. 2 Two angle measures for both △ABC and △XYZ are given. Using the given information about the triangles, is △ABC ∼ △XYZ? A. Yes, the triangles are similar by AA. B. No, because only 1 pair of corresponding angles are congruent. C. No, we cannot determine similarity without knowing the third angles. D. No, we cannot determine similarity without knowing the side ratios.

MAFS. 912. G-SRT. 1. 2 Determine if these two figures are similar. Which statements are true? Select all that apply. q q q There There was was was a a a dilation of scale factor 0. 5 centered at the origin. dilation of scale factor 1. 5 centered at the origin. translation left 0. 5 and up 1. 5. translation left 1. 5 and up 0. 5.

MAFS. 912. G-SRT. 1. 2

MAFS. 912. G-SRT. 1. 2 Which statements must be true? Select all that apply.

MAFS. 912. G-SRT. 1. 2 Select from the drop-down menus to support each line of the proof. The figures in pair 1 similar because

MAFS. 912. G-SRT. 1. 2 (continued from previous slide) The figures in pair 2 similar because The figures in pair 3 similar because

MAFS. 912. G-SRT. 1. 3 Enter your answer in the box.

MAFS. 912. G-SRT. 1. 3 Which statement is always true?

MAFS. 912. G-SRT. 2. 4 A. 15 B. 24 C. 25 D. 30

MAFS. 912. G-SRT. 2. 4 A. 5 B. 7 C. 8 D. 12

MAFS. 912. G-SRT. 2. 4

MAFS. 912. G-SRT. 2. 4 Which two steps are missing? Statements Reasons Angle-Angle Criterion Corresponding sides of similar triangles are proportional A B Multiplication property of equality C Segment Addition Postulate Substitution D Addition property of equality Distributive property Multiplication property of equality Distributive property

MAFS. 912. G-SRT. 2. 5

MAFS. 912. G-SRT. 2. 5 What is the height, in feet, of the 9 -foot ladder against the house?

MAFS. 912. G-SRT. 2. 5

MAFS. 912. G-SRT. 2. 5 Enter your answer in the box.

MAFS. 912. G-SRT. 2. 5 Similar triangles RST and UVW are shown in this diagram. Enter your answer in the box.

MAFS. 912. G-SRT. 2. 5 Jessica writes a proof as show. Which statement is a valid conclusion for Jessica’s proof?

MAFS. 912. G-SRT. 3. 6 Triangle ABC and DEF are right triangles, as shown. Triangle ABC is similar to triangle DEF.

MAFS. 912. G-SRT. 3. 6

MAFS. 912. G-SRT. 3. 6 Right triangle ABC is shown. What must be true about ∠A and ∠B? Select all that apply. q ∠A ≅ ∠B q ∠A and ∠B are complementary q ∠A and ∠B are supplementary q cos A = cos B q cos A = sin B q sin A = cos B q sin A = sin B

MAFS. 912. G-SRT. 3. 6 Consider the right triangle shown below.

MAFS. 912. G-SRT. 3. 6

MAFS. 912. G-SRT. 3. 7

MAFS. 912. G-SRT. 3. 7 Which statement must be true?

MAFS. 912. G-SRT. 3. 7

MAFS. 912. G-SRT. 3. 7 The figure below shows right triangles drawn inside of a rectangle. Select from the drop-down menus to correctly complete each statement.

MAFS. 912. G-SRT. 3. 8

MAFS. 912. G-SRT. 3. 8 The right triangle shown is missing the lengths of two sides. Enter the lengths of the two missing sides in the boxes below. Round your answers to the nearest tenth. Length of the hypotenuse: Length of the leg: cm cm

MAFS. 912. G-SRT. 3. 8 What is the horizontal distance d from the truck to the office building, rounded to the nearest tenth of a meter? A. 15. 4 m B. 16. 4 m C. 42. 3 m D. 123. 6 m

MAFS. 912. G-SRT. 3. 8 A submarine dives as shown in the diagram. Enter your answer in the box.

MAFS. 912. G-SRT. 3. 8 Twelve students are lined up to have their class picture taken. The photographer’s camera has a picture angle of 52°. The picture angle limits the width of the photo that can be taken. The line of students is approximately 26 feet long. About how far must the photographer be from the line of students in order to center all 12 students in the picture? A. 15 feet B. 27 feet C. 30 feet D. 53 feet

MAFS. 912. G-SRT. 3. 8 Bob places an 18 -foot ladder 6 feet from the base of his house and leans it up against the side of his house. Find, to the nearest degree, the measure of the angle the bottom of the ladder makes with the ground. Enter your answer in the box.

MAFS. 912. G-SRT. 3. 8 Triangle RST is shown.

MAFS. 912. G-SRT. 3. 8 Enter your answer in the box.

MAFS. 912. G-SRT. 3. 8 A. 48° B. 47° C. 43° D. 34°

MAFS. 912. G-SRT. 3. 8 A student stands 50 feet away from the front of a building and measures the angle of elevation to the top of the building. From the student’s eye level 5 feet off the ground, the angle of elevation to the top of the building is 30°. Approximately what is the height of the building? A. 25 feet B. 29 feet C. 30 feet D. 34 feet

MAFS. 912. G-SRT. 3. 8 From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11. 87°. To the nearest foot, what is the height of the monument? A. 543 B. 555 C. 1086 D. 1110

MAFS. 912. G-SRT. 3. 8 Consider this right triangle. Determine whether each expression can be used to find the length of side RS. Select Yes or No for each expression. Yes No

MAFS. 912. G-SRT. 3. 8 Enter your answer in the box.

MAFS. 912. G-SRT. 3. 8 (continued from previous slide) Enter your answer in the box. Part C: The bottom of Sam’s 30 -foot ladder is 6 feet from the base of the wall it is leaning against. If Sam moves the bottom of the ladder 1 foot farther away from the wall, which of the listed statements is true? A. The top of the ladder will move down by about 0. 22 foot. B. The top of the ladder will move down by about 1. 0 foot. C. The top of the ladder will move up by about 1. 22 feet. D. The top of the ladder will not move.

MAFS. 912. G-SRT. 3. 8 (continued from previous slide) Part D: The bottom of Sam’s 30 -foot ladder is 6 feet from the base of the wall it is leaning against. If Sam moves the bottom of the ladder 1 foot farther away from the wall, which of the listed statements is true? A. The angle the ladder makes with the ground will increase by about 3 degrees. B. The angle the ladder makes with the ground will decrease by about 1 degree. C. The angle the ladder makes with the ground will decrease by about 2 degrees. D. The angle the ladder makes with the ground will not change.

MAFS. 912. G-SRT. 3. 8 A 225 -foot support wire is attached to the top of a monument at a stake on the ground 100 feet from the base of the monument, as shown. Part A: What is the approximate height of the monument? A. 125 feet B. 202 feet C. 246 feet D. 325 feet

MAFS. 912. G-SRT. 3. 8 (continued from previous slide) Part B: What is the angle of elevation from the stake on the ground to the top of the monument? A. 24. 0° B. 26. 4° C. 63. 6° D. 66. 0°

Acknowledgment The assessment items presented in this Power. Point have been compiled from several free web-based resources like sample items, released items, and practice tests. • Regent Exams - http: //www. jmap. org/JMAP_REGENTS_EXAMS. htm • PARCC Released Items - https: //parcc-assessment. org/released-items/ • NCFE Released Items For High School Subjects (2017 -18) http: //www. ncpublicschools. org/accountability/testing/common-exams/releaseditems/highschoolitems • Ohio Student Practice Resources – Mathematics https: //oh. portal. airast. org/resources/mathematics-spr/