# UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

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1 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D' F' AB D' F' A' B' BC [Key: B] 2) Which transformation results in a figure that is similar to the original figure but has a greater area? A. a dilation of QRS by a scale factor of 0.25 B. a dilation of QRS by a scale factor of 0.5 C. a dilation of QRS by a scale factor of 1 D. a dilation of QRS by a scale factor of 2 [Key: D] 29

2 3) In the coordinate plane, segment PQ is the result of a dilation of segment XY by a scale factor of 1. 2 Which point is the center of dilation? A. ( 4, 0) B. (0, 4) C. (0, 4) D. (4, 0) [Key: A] 30

3 1) In the triangles shown, ABC is dilated by a factor of 2 3 to form XYZ. Given that m A 50 and m B 100, what is m Z? A. 15 B. 25 C. 30 D. 50 [Key: C] 2) In the triangle shown, GH DF. What is the length of GE? A. 2.0 B. 4.5 C. 7.5 D. 8.0 [Key: B] 34

4 3) Use this triangle to answer the question. This is a proof of the statement If a line is parallel to one side of a triangle and intersects the other two sides at distinct points, then it separates these sides into segments of proportional lengths. Which reason justifies Step 2? A. Alternate interior angles are congruent. B. Alternate exterior angles are congruent. C. Corresponding angles are congruent. D. Vertical angles are congruent. [Key: C] 35

5 1) Parallelogram FGHJ was translated 3 units down to form parallelogram F' G' H' J '. Parallelogram F' G' H' J ' was then rotated 90 counterclockwise about point G ' to obtain parallelogram F '' G'' H'' J ''. Which statement is true about parallelogram FGHJ and parallelogram F'' G'' H'' J ''? A. The figures are both similar and congruent. B. The figures are neither similar nor congruent. C. The figures are similar but not congruent. D. The figures are congruent but not similar. 2) Consider the triangles shown. [Key: A] Which can be used to prove the triangles are congruent? A. SSS B. ASA C. SAS D. AAS [Key: D] 40

6 3) In this diagram, JI and J. Which additional information is sufficient to prove that DEF is congruent to JIH? A. EF IH B. DH JF C. HG GI D. HF JF [Key: B] 41

7 1) In this diagram, CD is the perpendicular bisector of AB. The two-column proof shows that AC is congruent to BC. Step Statement Justification 1 CD is the perpendicular bisector of AB Given 2 AD BD Definition of bisector 3 CD CD Reflexive Property of Congruence 4 ADC and BDC are right angles Definition of perpendicular lines 5 ADC BDC All right angles are congruent 6 ADC BDC? 7 AC BC CPCTC Which theorem would justify Step 6? A. AAS B. ASA C. SAS D. SSS [Key: C] 45

8 2) In this diagram, STU is an isosceles triangle where ST is congruent to UT. The paragraph proof shows that S is congruent to U. It is given that ST is congruent to UT. Draw TV that bisects T. By the definition of an angle bisector, STV is congruent to UTV. By the Reflexive Property, TV is congruent to TV. Triangle STV is congruent to triangle UTV by SAS. S is congruent to U by?. Which step is missing in the proof? A. CPCTC B. Reflexive Property of Congruence C. Definition of right angles D. Angle Congruence Postulate [Key: A] 46

9 1) Consider the construction of the angle bisector shown. Which could have been the first step in creating this construction? A. Place the compass point on point A and draw an arc inside Y. B. Place the compass point on point B and draw an arc inside Y. C. Place the compass point on vertex Y and draw an arc that intersects YX and YZ. D. Place the compass point on vertex Y and draw an arc that intersects point C. [Key: C] 2) Consider the beginning of a construction of a square inscribed in circle Q. Step 1: Label point R on circle Q. Step 2: Draw a diameter through R and Q. Step 3: Label the intersection on the circle point T. What is the next step in this construction? A. Draw radius SQ. B. Label point S on circle Q. C. Construct a line segment parallel to RT. D. Construct the perpendicular bisector of RT. [Key: D] 59

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