Triangles Review Sheetms. Anderle
Name:______Date:______Period:______
Triangles Review SheetMs. 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) (3)
(2) (4)
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?
(1) 12(2) (3) 16(4)
9. In the diagram of ΔABC below, , 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(4) x + x = 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
16. In ΔABC, point D is on AB and point E is on BC, such that . If DB=2, DA=7, and DE=3, 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 triangle18. In isosceles triangle ABC, . If
are represented by 5x–7, 7x+6, and 4x–11. AC = 5x and CB = 2x + 30, find the value of x
Classify this triangle.and the length of AC.
19. In isosceles triangle ABC, . If 20. In triangle EFG, . If
AB = 5x+10, BC = 3x+40, and AC = 2x+30, find m<F = 2x+60, and m<G = 14x+30, find
the length of each side of the triangle.m<E, m<F, and m<G.
21. In triangle ABC, . If m<A=7x22. Given equilateral triangle FGH with
and m<C = 2x+50, find m<A and m<C., , and
, what is the measure of each
side of the triangle?
23. The measure of the larger acute angle 24. The measures of the angles of a triangle
of a right triangle is two times the measure are in the ratio of 2:3:1. Find each angle of
of the smaller acute angle. Find the measure the triangle. Classify this triangle.
of each angle.
25. Find the value of x in the diagram26. In triangle ABC, m<A = 9x, m<B = 3x-6,
below. and m<C = 11x+2, show that triangle ABC
is a right triangle.
27. The measure of the vertex angle of 28. Can 67°, 33°, and 50° represent the
an isosceles triangle exceeds the measure angles of a triangle? Why or why not?
of each base angle by 30. Find the measure
of each angle of the triangle.
29. In ΔABC, . The measure of an30. In ΔDEF, m<D = 2x+4, m<E = 6x – 58.
exterior angle at vertex C is represented by the measure of an exterior angle at F is
5x+10. If <A measure 30, find the value of x.represented by 5x. Find the value of x.
31. In ΔABC, m<C = 90 and m<B = 35. Name 32. In triangle ABC, AB=8, BC=10, and
the shortest side of the triangle.CA=14. Name the largest angle.
33. In triangle ABC, medians, , and 34. In triangle ABC, medians, , and
are concurrent at point P. If AP = 8, find are concurrent at point P.If AP=7x+1
the length of median .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. 38. In triangle HKL, m<HKL = 80˚.KR is an
Find the value of x.angle bisector.What is the value of x?
39. The intersection of the perpendicular40. The intersection of the angle bisectors is
bisectors is called the:called the:
41. The intersection of the altitudes of42. The intersection of the medians of a
a triangle is called the:triangle is called the:
43. What is the center of the circle that is44. What is the center of the circle that is
inscribed inside a triangle?circumscribed around a triangle?