36. Congruence and similarity.docx

Congruence and similarity 1. In the figure above, ​BC​​​ and ​AD​​​ are parallel. What is the length, in centimeters  (cm), of BF​​​? Correct answer: 10 Level: 3 2. Note: figure not drawn to scale Triangles JKL and RST are shown above. Angles are given in radians, to the nearest hundredth. What is the value of θ in radians, to the nearest tenth? Correct answer: 1.3 Level: 3 3. In the diagram above, triangle AFG is similar to triangle ABC. What is the measure of∠AGF, in degrees? Correct answer: 78 Level: 3 4. In the diagram at left, suppose a=23x. What is the measure of x? Correct answer: 54° Level: 3 5. In the diagram at left,  ​AD​​​ is congruent to BD​​​. Which of the following statements is true? A. AE​​​ bisects∠CAB B. ∠ACB is congruent to ∠ABC C. triangle ABC is isosceles D. AE​​​ is a median of △ABC Correct answer: C Level: 3 6. The diagram at left shows four lines: AB, CD, AD, and BC. Which of the following statements is true? A. ∠ABC measures 88​° B. ∠BCD measures 80​°​​ C. AD intersects BC D. AD is parallel to BC Correct answer: C Level: 4 7. In the diagram at left,  ​AB​​​ is congruent to ​BC​​​. Which of the following statements is true? A. ∠DAC is congruent to∠DCA B. ∠BAC is congruent to∠BCA C. ∠ABC is congruent to∠ADC D. ∠BAD is congruent to∠BCD Correct answer: B Level: 4 8. Isosceles triangles ABC and DEF shown above are similar triangles. The length AB equals the length BC, and the length DE equals the length EF. What is the value of v in radians, to the nearest hundredth? Correct answer: 2.09 Level: 4 9. Given the lengths of the segments in the figure above, what is the length, to the nearest tenth, of n? Correct answer: 425 Level: 4 10. In the figure at left, lines c and d are parallel. What is the value of x? Correct answer: 8 Level: 4 11. Note: figure not drawn to scale n Parallelogram ABCD shown above is congruent to parallelogram PQRS. What is the value of a in radians, to the nearest hundredth? Correct answer: 0.39 Level: 4 12. The diagram at left shows a rectangular billiard table with a width of 39inches (in) and a length of 78 in. A player is trying to shoot the red ball located at point H, into the corner pocket D by bouncing the ball off of a point R that is x inches from point B. The player knows that when the ball bounces off point R, ∠HRB will be congruent to ∠DRC. If the point BB is the midpoint of ​AC​​​ and the red ball is 15in above B, approximately what is the value of x? A. 7in B. 9in C. 11in D. 13in Correct answer: C Level: 4 13. Given the figure at left, which of the following statements must be true? A. AB​​​ is parallel toDE​​​. B. C is the midpoint of BD​​​. C. Triangle CBA is congruent to triangle CDE. D. ∠ABC and ∠DCE are vertical angles. Correct answer: A Level: 4 14. In triangle ABC shown at left, tick marks of equal number represent sides of equal length. Therefore, the point along line segment AB​​​ is the midpoint of AB​​​. What is the value of β in terms of α and t? A. α B. t C. π2 – α D. π2 – α Correct answer: B Level: 4 15. In the diagram at left, line v transverses lines w, x, y, and z. Given the angle measurements shown, which pair of lines is parallel? A. Lines w and x B. Lines y and z C. Lines w and y D. Lines x and z Correct answer: A Level: 4 16. Both square ABCD and square EFGH shown at left have center Q. However, they do not have the same area. Which of the following must be true? A. α​∘​​=w​∘​​ B. α​∘​​=−w​∘​​ C. α​∘​​=90​∘​​−w​∘​​ D. α​∘​​=180​∘​​−w​∘​​ Correct answer: A Level: 4