2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D.

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1 1. If two angles of a triangle measure 56 and 68, the triangle is A. scalene B. isosceles C. obtuse D. right 2. If two isosceles triangles have congruent vertex angles, then the triangles must be A. congruent B. right C. equilateral D. similar 3. In the accompanying diagram of AEB, EB is extended to R and K, and m 3 = m 4 = 135. Triangle AEB must be 4. If the measure of the angles of a triangle are represented by 2x, 4x, and 6x, then the triangle is A. right B. obtuse C. acute D. equiangular A. equilateral B. acute and isosceles C. obtuse and isosceles D. right and isosceles

2 5. Which diagram represents a correct construction of equilateral ABC, given side AB? A. B. 6. If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be A. obtuse B. right C. acute D. isosceles C. D. 7. In the diagram below of ABC, D is a point on AB, E is a point on BC, AC DE, CE = 25 inches, AD = 18 inches, and DB = 12 inches. Find, to the nearest tenth of an inch, the length of EB. 8. If the measures of three angles of a triangle are represented by (y + 30), (4y + 30), and (10y 30), then the triangle must be A. obtuse B. isosceles C. scalene D. right

3 9. Find the number of degrees in the measure of the vertex angle of an isosceles triangle if each base angle measures If one of the base angles of an isosceles triangle has a measure of 54, find the measure of the vertex angle. 11. If the base angle of an isosceles triangle measures 50, what is the number of degrees in the measure of the vertex angle? 12. The vertex angle of an isosceles triangle measures 70. Find the number of degrees in a base angle.

4 13. The vertex angle of an isosceles triangle measures 58. Find the measure of a base angle. 14. Find the measure of a base angle of an isosceles triangle whose vertex angle measures In isosceles triangle RST, R is the vertex angle, and m S = 77. Find m R. 16. In an isosceles triangle, the measure of a base angle is 65. Find the number of degrees in the measure of the vertex angle.

5 17. Side PQ of PQR is extended through Q to point T. Which statement is not always true? A. m RQT > m R B. m RQT > m P C. m RQT = m P + m R D. m RQT > m PQR 18. In right triangle ABC, C is a right angle and m B = 60. What is the ratio of m A to m B? 19. In the accompanying diagram, what is the measure of angle x? 20. In the accompanying diagram, AC = BC and m A = 80. Find m C.

6 21. In right triangle ABC, altitude CD is drawn to hypotenuse AB. If m A = 40, find m BCD. 22. In ABC, the measure of B is 21 less than four times the measure of A, and the measure of C is 1 more than five times the measure of A. Find the measure, in degrees, of each angle of ABC. 23. In ABC, m A = 95, m B = 50, and m C = 35. Which expression correctly relates the lengths of the sides of this triangle? A. AB < BC < CA B. AB < AC < BC C. AC < BC < AB D. BC < AC < AB 24. The two acute angles in an isosceles right triangle must measure A. 30 and 60 B. 35 and 55 C. 40 and 50 D. 45 and 45

7 25. The measures of the angles of a triangle are represented by (3x 20), (7x + 30), and (2x + 50). Find x. 26. The vertex angle of an isosceles triangle measures 15 degrees more than one of its base angles. How many degrees are there in a base angle of the triangle? A. 50 B. 55 C. 65 D In the diagram below, ABC is shown with AC extended through point D. 28. The number of degrees in the measures of the angles of a triangle are represented by x, 3x + 7, and 4x + 5. Find the value of x. If m BCD = 6x + 2, m BAC = 3x + 15, and m ABC = 2x 1, what is the value of x? A. 12 B C. 16 D

8 29. What is the measure of the largest angle in the accompanying triangle? 30. In right triangle ABC, m A = 2x + 2, m B = 7x + 7, and m C = 90. Find the value of x. A. 41 B C. 56 D In RST, RS = ST. If m R = 2x 10 and m S = x, find the value of x. 32. The measure of the vertex angle of an isosceles triangle is three times the measure of a base angle. Find the number of degrees in the measure of a base angle.

9 33. In the accompanying diagram of ABC, AB is extended through D, m CBD = 30, and AB = BC. 34. In ABC, BC is extended through C to D. If m A = 65, m B = 70, what is the measure of DCA? What is the measure of A? A. 15 B. 30 C. 75 D In the accompanying diagram of ABC, side AB is extended to D. If m ACB = x + 30, m CAB = 2x + 10, and m CBD = 4x + 30, what is the value of x? 36. In the accompanying diagram of BCD, m C = 70, m CDE = 130, and side BD is extended to A and to E. Find m CBA.

10 37. In the accompanying diagram, DAB is an exterior angle of ABC. If m DAB = 140 and m B = 60, find m C. 38. In the accompanying diagram of RET, side RT is extended through T to C. If m ETC = 6x + 10, m RET = x + 50, and m ERT = 4x 20, find the value of x. 39. If MAR is an equilateral triangle, find the measure of an exterior angle at R. 40. In the accompanying diagram of ABC, the measure of an exterior angle at C is 105 and m A = 35. Find m B.

11 41. The ratio of the measures of the angles of a triangle is 2 : 3 : 5. Find the measure of the smallest angle of the triangle. 42. The ratio of the measures of the angles of a triangle is 1 : 2 : 2. Find the measure of the smallest angle. 43. One angle of a triangle measures 30. If the measures of the other two angles are in the ratio 3 : 7, the measure of the largest angle of the triangle is A. 15 B. 105 C. 126 D The measures of the angles of a triangle are in the ratio 2 : 3 : 4. In degrees, the measure of the largest angle of the triangle is A. 20 B. 40 C. 80 D. 100

12 45. The measures of the acute angles of right triangle ABC are in the ratio 2 : 3. The measure of the smaller acute angle must equal A. 18 B. 36 C. 54 D If the measures of the angles of a triangle are in the ratio 1 : 3 : 5, the number of degrees in the measure of the smallest angle is A. 10 B. 20 C. 60 D If the measures of the angles of a triangle are in the ratio 2 : 3 : 4, the measure of the smallest angle is A. 20 B. 40 C. 60 D The measures of the three angles of a triangle are in the ratio 2 : 3 : 4. Find the measure of the largest angle of the triangle.

13 49. In ABC, m A = 3x + 40, m B = 8x + 35, and m C = 10π. Which is the longest side of the triangle? 50. In ABC, m A = 41, m B = 2x 37, and m C = 3x 29. Which side of the triangle is the shortest side? 51. In ABC, AB = 10 and BC = 5. Which expression can be true? A. AC = 5 B. AC = 20 C. AC < 5 D. AC > In RST, m R = 75 and m S = 20. Which is the longest side of the triangle?

14 53. In ABC, m A = 55 and AC < BC. Which angle is the largest angle of the triangle? 54. In MEC, an exterior angle at C measures 115, and the measure of M is 60. Which is the shortest side of MEC. 55. In ABC, m A = 60 and m B = 40. Which side of ABC is longest? 56. What is the length of the altitude of an equilateral triangle whose side has length 4? A. 2 3 B. 2 C. 4 3 D. 4

15 57. Which set of numbers may be the measure of the sides of a triangle? A. {10, 10, 20} B. {4, 6, 12} C. {2, 4, 6} D. {8, 10, 12} 58. If the lengths of two sides of a triangle are 6 and 8, the length of the third side may be A. 7 B. 2 C. 14 D Which set may be the lengths of the sides of an isosceles triangle? A. {1, 1, 2} B. {3, 3, 8} C. {5, 12, 13} D. {4, 4, 6} 60. Which set of numbers could not represent the lengths of the sides of a right triangle? A. { } 1, 3, 10 B. {2, 3, 4} C. {3, 4, 5} D. {8, 15, 17}

16 61. Which set of numbers can not represent the sides of a triangle? A. {2, 3, 4} B. {3, 4, 5} C. {3, 2, 1} D. {4, 3, 4} 62. If the lengths of two sides of a triangle are 2 and 5, the length of the third side could be A. 1 B. 2 C. 6 D Which set of numbers can not represent the lengths of the sides of a triangle? A. {6, 8, 11} B. {7, 5, 6} C. {7, 18, 11} D. {9, 12, 19} 64. Two sides of a triangle have lengths 5 and 8. Which length can not be the length of the third side? A. 5 B. 6 C. 3 D. 4

17 Problem-Attic format version c EducAide Software Licensed for use by kristen farrelly Terms of Use at Triangle flashcards 5/23/ B D D A A A B D m A = 20, m B = 59, and m C = B D B A D A m CBA =

18 Teacher s Key Page B 44. C 45. B 46. B 47. B AC 50. BC 51. D 52. RS 53. C 54. MC 55. AB or c 56. A 57. D 58. A 59. D 60. B 61. C 62. C 63. C 64. C

GEOMETRY Teacher: Mrs. Flynn Topic: Similarity. Teacher: Mrs. Flynn Topic: Similarity

GEOMETRY Teacher: Mrs. Flynn Topic: Similarity Name: Date: Teacher: Mrs. Flynn Topic: Similarity 1. A tree casts a shadow 24 feet long at the same time a man 6 feet tall casts a shadow 4 feet long. Find