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Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. 2. 3. In a plane, lines that never meet are called . A. parallel B. perpendicular C. congruent D. intersecting E. concentric In the drawing, what is the measure of angle y? The two angles formed as a result of a . bisector will always be A. complementary B. supplementary C. right D. congruent A. 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 ? A. D. 4. 5. h m ; 2 2 (h; m) B. ( h; 2m) E. ( h; m) C. 40 B. 60 C. 80 D. 100 6. Solve for x and y. Show all work. 7. Which of the following sets of points are collinear? (2h; m) ! ! In the gure, AB is parallel to CD and OBDC is right. Which of the following statements may be false? A. AB ? BD B. measure of O3 is less than 90 C. O2 and O 4 are supplementary D. O1 and O 3 are congruent page 1 A. A, B, D B. A, B, C C. B, D, C D. D, A, C E. C, A, D 8. Lines t1 , t2 , and t3 are parallel lines intersected by line t4 . What is the measure of Os? A. 42 B. 48 C. D. Not enough information. 12. Which type of triangle is ^ABC ? A. Right B. Isosceles C. Scalene D. Equilateral 138 13. Given the gure and the following information: AN k SK and AS k NK 9. Find x. mOA = 5x + 6 mODAS = 3x + 50 mON = 3y A. 10. 11. Score 50 B. 80 C. 110 D. 10 Find the value of x and y. 120 In the diagram, what is the sum of the measures of OB and OD? A. 90 B. 95 C. 102.5 D. 112.5 E. 142.5 In the gure below, what is the measure of OB ? A. 35 B. 40 C. 71 D. 76 E. 105 page 2 Triangle Congruence and Similarity Review 14. In the gure, lines B and C are parallel. alternate interior adjacent alternate exterior corresponding supplementary 16. BC = 4. Proof the triangles are similar. vertical Statements complementary Reason a) Use the terms in the box to label each angle pair. More than one term may apply to each angle pair. O1, O2 O2, O4 O3, O 5 O2, O 6 b) If mO3 = 9x and mO8 = 6x, nd the measure of each numbered angle in the gure. 17. 15. Score In the diagram, if lines a and b are parallel, which of the following must be true? A. O2 = O5 B. O3 = O4 C. O7 = O1 D. O4 = O5 E. O8 = O2 Given: AD bisects BC AE = DE Prove: AB k CD Statements Reason Flowchart Proof: page 3 Triangle Congruence and Similarity Review 19. 18. Given: CF = EF FD is a median of ^CFE Given: AD is the perpendicular bisector of BC Prove: ^ABC is isosceles Statement Prove: CD = ED Two-Column Proof: given 2. def'n of ? bisector 3. def'n of ? bisector 4. Statements Reason 1. AD is ? bisector of BC All right angles are congruent 5. AD = AD Reason 6. ^ABD = ^ ACD 7. AB = AC SAS 8. ^ABC is isosceles Fill in the blanks. Then write a owchart proof. Paragraph Proof: Score page 4 Triangle Congruence and Similarity Review 22. 20. Given: AB k DC AB = DC Prove: mODAC = mOBCA To test this conjecture, which pair of congruent angles are alternate interior angles? Two Column Proof: Paragraph Proof: Statements Reasons 23. Flowchart Proof: 21. 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. 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. 24. A. O1 and O4 B. O2 and O8 C. O4 and O8 D. O3 and O5 Which of these pairs of triangles must be similar? A. two right triangles where the length of each hypotenuse is 3 B. two acute triangles with two pairs of corresponding, congruent sides 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 Given: ST k QR Prove: ^PST ^PQR Which of these congruent angles are corresponding angles? Score A. O1 and O 4 B. O1 and O3 C. O4 and O 8 D. O4 and O3 page 5 Triangle Congruence and Similarity Review 25. In the gure 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, OPST = OPTS Prove: ^PQR is isosceles. Statements Score Reasons page 6 Triangle Congruence and Similarity Review 27. Given that triangle ABC is similar to triangle DEC, OABC corresponds to: A. OCDE B. ODEC C. OACB D. OECD 28. 29. 30. In the gure, DE k BC. Which proportion is not true? A. AD AE = BA CA B. AD AB = AE AC C. DB BA = EC CA D. AD AE = DB AC In the gure, TU k QR. Which proportion is not true? A. TU QR = RS US B. QR TU = QS TS C. RU US = QR TU D. ST SQ = TU QR In the diagram, mOD = OE. Which of the following statements are true for this diagram? I. ^ADC ^BEC II. ^ADC ^EBC III. AD k BE Score page 7 A. I only B. II only C. III only D. I and II E. I and III Triangle Congruence and Similarity Review 31. 35. In the diagram, CD ? AC, BE ? AC, AE = 17, BE = 8, and CD = 32. Find DE. A. 35 B. 45 D. 60 E. 68 C. 51 36. 32. 33. A. 16 B. 17 C. 19 D. 20 E. 21 The SAS congruency axiom states that two triangles are congruent if: 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. D. two sides and the excluded angle of one triangle are equal to two sides and the excluded angle of the other triangle. PQ is parallel to XY . What is the length of XY in centimeters? A. 6 B. 5 31 C. 4 D. 3 E. 2 In the diagram, AD = DC, DE k AB, and DE = 4. Find AB. A. 2 B. 4 C. 6 D. 8 E. 16 37. 34. Find the length of side x. Collin wants to nd the width of a creek. He takes some measurements and creates a diagram. In the diagram, DE k AB, CA = 9, DA = 3, and CE = 10. Find EB. A. 2.5 B. 3 C. 4 D. 4.5 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, nd 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: Statements Reasons 40. Two Column Proof: Paragraph Proof: Statements 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 Prove: 41. Given: VT bisects RW RW bisects TV Prove: ^RSV = ^WST statement 1. 2. 3. 4. 5. 6. 7. 8. Two Column Proof: Paragraph Proof: Statements AB k ED Reasons reason AC is the median to BE BC = CE mO1 = mO2 EC is the median to AD AC = CD ^ACB = ^DCE mO3 = mO4 AB k ED Flowchart Proof: Score page 10 Triangle Congruence and Similarity Review