Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel B. perpendicular C. congruent D. intersecting E. concentric 2. The two angles formed as a result of a bisector will always be. A. complementary B. supplementary C. right D. congruent A. 40 B. 60 C. 80 D. 100 3. A line segment has A and B as its endpoints and M as its midpoint. If A has coordinates (h, 0) and B has coordinates (0, m), what are the coordinates of M? 6. Solve for x and y. Show all work. A. ( h 2, m ) 2 B. ( h, 2m) C. (2h, m) D. (h, m) E. ( h, m) 4. In the figure, AB is parallel to CD and BDC is right. Which of the following statements may be false? 7. Which of the following sets of points are collinear? A. A, B, D B. A, B, C A. AB BD B. measure of 3 is less than 90 C. 2 and 4 are supplementary C. B, D, C D. D, A, C E. C, A, D D. 1 and 3 are congruent page 1
8. Lines t 1, t 2, and t 3 are parallel lines intersected by line t 4. What is the measure of s? 12. Which type of triangle is ABC? A. Right B. Isosceles A. 42 B. 48 C. 138 D. Not enough information. 9. Find x. C. Scalene D. Equilateral 13. Given the figure and the following information: AN SK and AS NK m A = 5x + 6 m DAS = 3x + 50 m N = 3y 10 A. 50 B. 80 C. 110 D. 120 Find the value of x and y. 10. In the diagram, what is the sum of the measures of B and D? A. 90 B. 95 C. 102.5 D. 112.5 E. 142.5 11. In the figure below, what is the measure of B? A. 35 B. 40 C. 71 D. 76 E. 105 Score page 2 Triangle Congruence and Similarity Review
14. In the figure, lines B and C are parallel. alternate interior alternate exterior adjacent corresponding vertical supplementary complementary 16. BC = 4. Proof the triangles are similar. Reason a) Use the terms in the box to label each angle pair. More than one term may apply to each angle pair. 1, 2 2, 4 3, 5 2, 6 b) If m 3 = 9x and m 8 = 6x, find the measure of each numbered angle in the figure. 15. In the diagram, if lines a and b are parallel, which of the following must be true? 17. Given: AD bisects BC AE = DE AB CD A. 2 = 5 B. 3 = 4 C. 7 = 1 D. 4 = 5 E. 8 = 2 Flowchart Proof: Reason Score page 3 Triangle Congruence and Similarity Review
19. Given: AD is the perpendicular bisector of BC 18. Given: CF = EF FD is a median of CFE CD = ED Two-Column Proof: Reason ABC is isosceles Statement 1. AD is bisector of BC given Reason 2. def n of bisector 3. def n of bisector 4. All right angles are congruent 5. AD = AD 6. ABD = ACD SAS 7. AB = AC 8. ABC is isosceles Paragraph Proof: Fill in the blanks. proof. Then write a flowchart Score page 4 Triangle Congruence and Similarity Review
22. The Corresponding Angles Conjecture states that if two parallel lines are cut by a transversal, the alternate interior angles are congruent. The picture below shows this relationship. 20. Given: AB DC AB = DC m DAC = m BCA Two Column Proof: Paragraph Proof: To test this conjecture, which pair of congruent angles are alternate interior angles? Reasons A. 1 and 4 B. 2 and 8 C. 4 and 8 D. 3 and 5 23. Which of these pairs of triangles must be similar? Flowchart Proof: A. two right triangles where the length of each hypotenuse is 3 B. two acute triangles with two pairs of corresponding, congruent sides 21. The Corresponding Angles Conjecture states that if two parallel lines are cut by a transversal, the corresponding angles are congruent. The picture below shows this relationship. C. two right triangles, one whose sides are in the ratio 3 : 4 : 5 and the other 5 : 12 : 13 D. two triangles, one with sides x, y and z, and the other with sides 2x, 2y, and 2z 24. Given: ST QR PST PQR Which of these congruent angles are corresponding angles? A. 1 and 4 B. 1 and 3 C. 4 and 8 D. 4 and 3 Score page 5 Triangle Congruence and Similarity Review
25. In the figure shown, segment AC is perpendicular to segment BC in triangle ACB. Segment FE is parallel to segment BC. If AF = 12, FB = 8 and FE = 9, a) What is the length of segment BC? b) Why is segment FE perpendicular to segment AC? 26. Given: SQ = TR, PST = PTS PQR is isosceles. Reasons Score page 6 Triangle Congruence and Similarity Review
27. Given that triangle ABC is similar to triangle DEC, ABC corresponds to: 28. In the figure, DE BC. Which proportion is not true? A. CDE B. DEC C. ACB D. ECD A. AD BA = AE CA B. AD AE = AB AC C. DB EC = BA CA D. AD DB = AE AC 29. In the figure, TU QR. Which proportion is not true? A. QR RS = TU US B. QR QS = TU TS C. RU QR = US TU D. ST TU = SQ QR 30. In the diagram, m D = E. Which of the following statements are true for this diagram? I. ADC BEC II. III. ADC EBC AD BE A. I only B. II only C. III only D. I and II E. I and III Score page 7 Triangle Congruence and Similarity Review
31. In the diagram, CD AC, BE AC, AE = 17, BE = 8, and CD = 32. Find DE. A. 35 B. 45 C. 51 D. 60 E. 68 35. Find the length of side x. A. 16 B. 17 C. 19 D. 20 E. 21 36. The SAS congruency axiom states that two triangles are congruent if: 32. PQ is parallel to XY. What is the length of XY in centimeters? A. 6 B. 5 1 3 C. 4 D. 3 E. 2 A. two angles and the contained side of one triangle are equal to two angles and the contained angle of the other triangle. B. two sides and the contained angle of one triangle are equal to two sides and the contained angle of the other triangle. C. two angles and a side of one triangle are equal to two angles and a side of the other triangle. 33. In the diagram, AD = DC, DE AB, and DE = 4. Find AB. A. 2 B. 4 C. 6 D. 8 E. 16 D. two sides and the excluded angle of one triangle are equal to two sides and the excluded angle of the other triangle. 37. In the diagram, DE AB, CA = 9, DA = 3, and CE = 10. Find EB. A. 2.5 B. 3 C. 4 D. 4.5 34. Collin wants to find the width of a creek. He takes some measurements and creates a diagram. E. 5 38. V and Y are midpoints of TW and TX, and U and Z are midpoints of TV and TY. If VY = 7, find the length of UZ. A. 3.5 B. 14 C. 21 D. 10.5 Assuming that AC is perpendicular to CD and CD is parallel to BE, what is the width of the creek to the nearest meter? Show all your work. Score page 8 Triangle Congruence and Similarity Review
39. Two Column Proof: Paragraph Proof: Reasons 40. Two Column Proof: Paragraph Proof: Flowchart Proof: Reasons Flowchart Proof: Score page 9 Triangle Congruence and Similarity Review
42. Fill in the reasons for the proof. Given: AC is the median to BE EC is the median to AD AB ED 41. Given: VT bisects RW RW bisects TV RSV = WST Two Column Proof: Paragraph Proof: Reasons statement 1. AC is the median to BE 2. BC = CE 3. m 1 = m 2 4. EC is the median to AD 5. AC = CD 6. ACB = DCE 7. m 3 = m 4 8. AB ED reason Flowchart Proof: Score page 10 Triangle Congruence and Similarity Review