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Name:___________________________________ Triangles Review Sheet Date:_______ Period:______ Ms. Anderle Triangles Review Sheet Regents Multiple Choice Questions: 1. In the diagram below, the vertices of ΔDEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter ΔABC is 36 cm. What is the length, in centimeters of EF? (1) 6 (2) 12 (3) 18 (4) 4 2. In ΔABC, AB = 7, BC = 8, and AC = 9. Which list has the angles of ΔABC in order from smallest to largest? (1) <A, <B, <C (2) <B, <A, <C (3) <C, <B, <A (4) <C, <A, <B 3. In the diagram below of ΔABC, medians AD, BE, and CF intersect at G. If CF = 24, what is the length of FG? (1) 8 (2) 10 (3) 12 (4) 16 4. In isosceles triangle ABC, AB = BC. Which statement will always be true? (1) m<B = m<A (2) m<A > m<B (3) m<A = m<C (4) m<C < m<B 5. In ΔPQR, PQ = 8, QR = 12, and RP = 13. Which statement about the angles of ΔPQR must be true? (1) m∡𝑄 > m∡𝑃 > m∡𝑅 (3) m∡𝑅 > m∡𝑃 > m∡𝑄 (2) m∡𝑄 > m∡𝑅 > m∡𝑃 (4) m∡𝑃 > m∡𝑅 > m∡𝑄 6. In the diagram below of ΔABC, CD is the bisector of <BCA, AE is the bisector of <CAB, and BG is drawn. Which statement must be true? (1) DG = EG (2) AG = BG (3) m<AEB = m<AEC (4) m<DBG = m<EBG 7. In ΔABC, m<A = x, m<B = 2x + 2, and m<C = 3x + 4. What is the value of x? (1) 29 (2) 31 (3) 59 (4) 61 8. In the diagram below, ΔABC is shown with AC extended through point D. If m<BCD = 6x + 2, m<BAC = 3x + 15, and m<ABC = 2x – 1, what is the value of x? 10 (1) 12 (2) 14 11 (3) 16 (4) 18 1 9 9. In the diagram of ΔABC below, ̅̅̅̅ 𝐴𝐵 ≅ ̅̅̅̅ 𝐴𝐶 , the measure of <B is 40°. What is the m<A? (1) 40° (2) 50° (3) 70° (4) 100° 10. Which set of numbers represent the lengths of the sides of a triangle? (1) {5, 18, 33} (2) {6, 17, 22} (3) {16, 24, 7} (4) {26, 8, 15} 11. In the diagram below of ΔACT, D is the midpoint of AC, O is the midpoint of AT, and G is the midpoint of CT. If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG? (1) 21 (2) 25 (3) 32 (4) 40 12. Juliann plans on drawing ΔABC, where the measure of <A can range from 50° to 60° and the measure of <B can range from 90° to 100°. Given these conditions, what is the correct range of measures possible for <C? (1) 20° to 40° (2) 30° to 50° (3) 80° to 90° (4) 120° to 130° 13. In ΔABC, m<A = 95, m<B = 50, and m<C = 35. Which expression correctly relates the lengths of the sides of this triangle? (1) AB < BC < CA (2) AB < AC < BC (3) AC < BC < AB (4) BC < AC < AB 14. In the diagram of ΔABC below, Jose found the centroid P by constructing the three medians. He measured CF and found it to be 6 inches. If PF = x, which equation can be used to find x? (1) x + x = 6 (2) 3x + 2x = 6 (3) 2x + x = 6 2 (4) x + 3x = 6 15. Side PQ of ΔPQR is extended through Q to point T. Which statement is not always true? (1) m<RQT > m<R (3) m<RQT = m<P + m<R (2) m<RQT > m<P (4) m<RQT > m<PQR ̅̅̅̅. If DB=2, DA=7, and DE=3, 16. In ΔABC, point D is on AB and point E is on BC, such that ̅̅̅̅ 𝐷𝐸 ||𝐴𝐶 what is the length of AC? (1) 8 (2) 9 (3) 10.5 (4) 13.5 Free-Response Questions: 17. The measures of the angles of a triangle are represented by 5x–7, 7x+6, and 4x–11. Classify this triangle. 18. In isosceles triangle ABC, AC CB . If AC = 5x and CB = 2x + 30, find the value of x and the length of AC. 19. In isosceles triangle ABC, AB BC . If AB = 5x+10, BC = 3x+40, and AC = 2x+30, find the length of each side of the triangle. 20. In triangle EFG, EF FG . If m<F = 2x+60, and m<G = 14x+30, find m<E, m<F, and m<G. 21. In triangle ABC, AB BC . If m<A=7x and m<C = 2x+50, find m<A and m<C. 22. Given equilateral triangle FGH with FG 2 y 5 , GH 3 y 3 , and FH 5 y 19 , what is the measure of each side of the triangle? 23. The measure of the larger acute angle of a right triangle is two times the measure of the smaller acute angle. Find the measure of each angle. 24. The measures of the angles of a triangle are in the ratio of 2:3:1. Find each angle of the triangle. Classify this triangle. 25. Find the value of x in the diagram below. 26. In triangle ABC, m<A = 9x, m<B = 3x-6, and m<C = 11x+2, show that triangle ABC is a right triangle. 27. The measure of the vertex angle of an isosceles triangle exceeds the measure of each base angle by 30. Find the measure of each angle of the triangle. 28. Can 67°, 33°, and 50° represent the angles of a triangle? Why or why not? 29. In ΔABC, AC BC . The measure of an exterior angle at vertex C is represented by 5x+10. If <A measure 30, find the value of x. 30. In ΔDEF, m<D = 2x+4, m<E = 6x – 58. the measure of an exterior angle at F is represented by 5x. Find the value of x. 31. In ΔABC, m<C = 90 and m<B = 35. Name the shortest side of the triangle. 32. In triangle ABC, AB=8, BC=10, and CA=14. Name the largest angle. 33. In triangle ABC, medians AD , BE , and CF are concurrent at point P. If AP = 8, find the length of median AD . 34. In triangle ABC, medians AD , BE , and CF are concurrent at point P. If AP=7x+1 and DP = 4x-2, then what is the value of x? 35. The circumcenter of ΔABC is point P. If 36. In triangle ABC, CD is median to side AB. AP=x+2y, BP = 40, and CP = x + 4, find x and y. If AB = 16 and BD = 2x, what is the value of x? 37. In the diagram below JK is an altitude. Find the value of x. 38. In triangle HKL, m<HKL = 80˚. KR is an angle bisector. What is the value of x? 39. The intersection of the perpendicular bisectors is called the: 40. The intersection of the angle bisectors is called the: 41. The intersection of the altitudes of a triangle is called the: 42. The intersection of the medians of a triangle is called the: 43. What is the center of the circle that is inscribed inside a triangle? 44. What is the center of the circle that is circumscribed around a triangle?