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Name: ______________________________________________ Date: ___________________ Period: _______ Chapter 4 Review – Geometry 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 5.5, 5.6 Matching _______ 1. isosceles triangle A. triangle with all angles congruent _______ 2. equiangular triangle B. triangle with no congruent sides _______ 3. scalene triangle C. triangle with one right angle _______ 4. right triangle D. angle formed by extending side of ∆ _______ 5. equilateral triangle E. triangle with all sides congruent _______ 6. obtuse triangle F. triangle with all angles less than 90 _______ 7. acute triangle G. triangle with one angle greater than 90 _______ 8. exterior angle of ∆ H. triangle with at least 2 congruent sides Find the values of the variables. 9. _______ a d 120° a _______ b f _______ c c _______ d e 115° e b _______ e _______ f _______ g 20° 68° g 102° 70° 40° _______ j _______ k 45° j 50° k m _______ m 2013-2014: Geometry Unit IV Review Page 1 Classify each triangle by (s) sides and (a) angles. 10. 8 6 10 (s) ____________ (s) ____________ (s) ____________ (s) ____________ (a) ____________ (a) ____________ (a) ____________ (a) ____________ Solve for x and find the measure of each angle. B 11. (4x – 20)° x = __________ m A = __________ A (6x – 60)° (3x)° C m B = __________ m C = __________ True or False. Write out the word. _______ 12. All equilateral triangles are isosceles triangles. _______ 13. A triangle may have two right angles. _______ 14. The acute angles of a right triangle are complementary. Find the measure of each angle. _______ 15. m BCA D _______ 16. m DCE B _______ 17. m DEF _______ 18. m BCD G _______ 19. m BAG _______ 20. m GAH 50° A H C E F For #15-20 2013-2014: Geometry Unit IV Review Page 2 Name the congruence pattern that would prove the triangles congruent. You may mark vertical angles or shared sides as necessary. _______ 21. 21. 22. 23. 25. 26. 28. 29. 31. 32. _______ 22. _______ 23. _______ 24. 24. _______ 25. _______ 26. _______ 27. 27. _______ 28. _______ 29. _______ 30. 30. _______ 31. _______ 32. Is it possible for a triangle to have sides with the given lengths? Yes or No. _______ 33. 3, 4, 7 _______ 34. 11, 12, 23 _______ 35. 8, 15, 27 _______ 36. 1.5, 2, 3.75 2013-2014: Geometry Unit IV Review Page 3 Put the angles in order from largest to smallest _______ 37. 37. 2m _______ 38. X A 17 ft B W _______ 3.9 m 29 ft 37 ft 2.8 m _______ 38. C Y _______ _______ Put the sides in order from smallest to largest. _______ 39. 39. _______ _______ T 40. T 56º S 17. 7Iº _______ 40. U S 58º 62º U _______ _______ Informal Proofs. 41. MS LS , ES BS . M 1 a. Mark the triangles with the given information. b. What else is congruent? B E S 2 L c. Why are the triangles congruent? 2013-2014: Geometry Unit IV Review Page 4 42. P is the midpt of RS , and R S. T R a. Mark the triangles with the given information. b. What else is congruent? P 1 2 S V c. Why are the triangles congruent? d. Explain why T V? A Formal Proofs 43. F 4 3 Given: 1 2; 3 4; C is midpt of BE Prove: ∆ABC ∆FEC 1 B 2 A 44. Given: A E; C is midpt of BD B 1 Prove: ∆ACB ∆ECD 2 D E C C E 2013-2014: Geometry Unit IV Review Page 5 45. In ∆ CAT, CA = 12, AT = 15, and CT = 17. Which list has the angles of ∆CAT in order from smallest to largest? A. ∡ C, ∡ A, ∡ T B. ∡ A, ∡ C, ∡ T C. ∡ T, ∡ C, ∡ A D. ∡ T, ∡ A, ∡ C 46. Find m ∡ D O 4x° (9x-20)° G D 47. Find the measure of the smallest interior angle. (5x-15)° 105° (6x-12)° 48. Juan plans on drawing ∆QUE, such that the measure of ∡Q can range from 42° to 47°, and the measure of ∡ U can range from 38° to 46°. Given these conditions, what is the correct range of measures possible for ∡E? 2013-2014: Geometry Unit IV Review Page 6 49. In the figure below, ̅̅̅̅ ̅̅̅̅̅ bisect each other at A. B T A M N Is ∆BAT ≅ ∆MAN? ______________ By what Triangle Congruence Postulate or Theorem? ________________________________________ What else must then also be true by CPCTC? _______________________________________________ ____________________________________________________________________________________ 2013-2014: Geometry Unit IV Review Page 7