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?