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Transcript
Geometry: Unit 3 Review Name: ______________________________ Date: _________________ Hour: ____ Identify the choice that best completes the statement or answers the question. ____ 1. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. ____ 2. Name the theorem or postulate that lets you immediately conclude A B ( ( D C a. ASA b. AAS c. SAS d. none of these ____ 3. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II ____ 4. Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II ____ 5. Which group contains triangles that are all similar? a. b. 13 7 7 ) 32° 7 ) 45° 7 ) 53° 53° ) ) 45° d. c. ____ 6. In the diagram below, bisects 9 . Which of these would be necessary to justify that Angle-Side-Angle Congruency Theorem? a. c. b. d. is congruent to by the bisects ____ 7. Emilio had a map of the zoo. He noticed that when he connected the points for the places he wanted to go to, it created two similar triangles. Using the given diagram, which of the following explains why ? a. Angle-Angle Similarity Postulate c. Side-Side-Side Similarity Postulate b. Side-Angle-Side Similarity Postulate d. Transitive Property of Similarity. 8 ____ 8. Which steps correctly state how to construct the circumscribed circle (also called circumcircle) of a triangle? a. . b. To find the center of the To find the center of the c. circumscribed circle, find the point circumscribed circle, find the point of concurrence of the three internal of concurrence of the three angle bisectors. The radius of the altitudes. The radius of the circle is circle is the segment that joins the the segment that joins the center center and one side of the triangle and one of the vertices of the and is perpendicular to the side. triangle. To find the center of the To find the center of the d. circumscribed circle, find the point circumscribed circle, find the point of concurrence of the three of concurrence of the three medians of the triangle. The radius perpendicular bisectors. The radius of the circle is the segment that of the circle is the segment that joins the center and one of the joins the center and one of the vertices of the triangle. vertices of the triangle. Short Answer 9. Classify the triangle by its sides. The diagram is not to scale. 9 7 9 10. Classify ABC by its angles, when m A = 36, m B = 89, and m C = 55. 11. The triangular playground has angles whose measures are in the ratio 7 : 2 : 3. What is the measure of the smallest angle? 61° 12. Find the value of x. The diagram is not to scale. 106° x° 119° 13. Find the value of the variable. The diagram is not to scale. 49° x° 14. If BCDE is congruent to OPQR, then is congruent to U V 15. Use the information given in the diagram. Tell why and X W 16. 17. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to scale. d° 21° g 25 b f° e° 7 18. Given 24 69° c and , find the length of QS and TV. N 19. Name the angle included by the sides M and P 20. Justify the last two steps of the proof. Given: Prove: R and S Proof: 1. 2. 1. Given 3. 4. 3. 4. T 2. Given U A ( ( 21. Find the values of x and y. | | y° x° B 54° D C Drawing not to scale 22. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 58°? E | 23. Use the information in the figure. Find D 106° | F Drawing not to scale 24. What additional information will allow you to prove the triangles congruent by the HL Theorem? A B | C D | E 36 25. Find the value of x. The diagram is not to scale. x 36 34 32 26. Points B, D, and F are midpoints of the sides of The diagram is not to scale. 32 EC = 34 and DF = 19. Find AC. A B F C E D 27. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 190 ft 28. In ABC, G is the centroid and BE = 12. Find BG and GE. C B A C | 29. Name a median for G ) | F ) E H D G F D E 30. Name the point of concurrency of the angle bisectors. 31. Find the length of , given that is a median of the triangle and AC = 60. D A B C 32. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides • bisectors of the angles • medians • lines containing the altitudes. 33. What is the name of the segment inside the large triangle? 34. Find the area. The figure is not drawn to scale. 7 cm 4.4 cm 35. Figure . Name a pair of corresponding sides? 36. ABCD ~ WXYZ. AD = 12, DC = 6, and WZ = 52. Find YZ. The figures are not drawn to scale. X B W A Z C D Z 37. Triangles ABC and DEF are similar. Find the lengths of AB and EF. A D 5x 5 x F E B 4 C 38. Write a similarity statement for the triangles. D 53° G 60° C 60° E F 67° H 39. State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. B 5 O 12 5 7.5 A M 8 7.5 C N 40. Explain why the triangles are similar. Then find the value of x. ) x 8 ) 15 9 Not drawn to scale Geometry: Unit 3 Review Answer Key MULTIPLE CHOICE 22. 64° 23. 37° 1. D 2. A 3. A 24. 4. A 25. 68 5. A 26. 38 6. A 27. 95 ft 7. A 28. 8. D 29. SHORT ANSWER 9. isosceles 10. acute 11. 30 12. 45 13. 12 30. 31. 32. 34. 15.4 cm2 Reflexive Property, Given 16. 21 18. 10 37. AB = 10; EF = 2 38. 19. 21. 35. 36. 26 17. 20. circumcenter incenter centroid orthocenter 33. angle bisector 14. 15. C 30 39. Reflexive Property of ; SSS ; SSS 40. AA Postulate; 4 4 5