Similar Triangles & Types of Triangles

2018 December(B05) Math Question 2

2019 April(Z15) Math Question 3

2010 December(69A) Math Question 6

2025 October(J08) Math Question 6

8. In the figure shown below, AC II DE; BD = AD; D and E are on AB and BC, respectively; AC = 8 feet; and the height of AABC is 10 feet. What is DE, in feet?

2018 June(A11) Math Question 8

2011 June(69F) Math Question 8

9. In the figure shown below, E and G lie on AC, D and F lie on AB, DE and FG are parallel to BC, and the given lengths are in feet. What is the length of AC, in feet?

2021 April(Z04) Math Question 9

9. In ABC below, D is on AB, E is on AC, and ED || CB. If it can be determined, what is the ratio of the area of ABC to the area of ADE ?

2015 April(73G) Math Question 9

11. The lengths of corresponding sides of 2  similar right triangles are in the ratio 4:5. The hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?

Similar Triangles

2021 December(E23) Math Question 11

13. In the figure shown below, E and G lie on AC, D and F lie on AB, DE and FG are parallel to BC, and the given lengths are in feet. What is the length of AC, in feet?

2017 June(74C) Math Question 13

2018 December(B05) Math Question 16

16. In ABC shown below, the measure of LA is 48°, and AB AC. What is the measure of LC ?

2016 December(74H) Math Question 16

18. In isosceles triangle ABC, AB is congruent to BC and the measure of the vertex angle, B, is 75. What is the measure of A?

2014 December(72G) Math Question 18

Given △RST with RS = 18 cm, ST = 12 cm, and RT = 27 cm, which of the following statements is true about the angles of this triangle?

2025 October(J08) Math Question 19

2012 June(70C) Math Question 20

21. The perimeter of a certain scalene triangle is 100 inches. The side lengths of the triangle are represented by 5x, 3x + 30, and 2x + 10, respectively. What is the length, in inches, of the longest side of the triangle?

2018 June(A11) Math Question 21

22. In the figure shown below, AE || DC, AC and DE intersect at B, and the given lengths are in feet. What is the length, in feet, of BC ?

2015 June(73C) Math Question 22

24. What is the ratio of the total area of the bowling lane to the area of the pin deck?

2017 December(A10) Math Question 24

24. In ABC below, D is the midpoint of CB, ZABC is a right angle, AB = 8 m, and AC = 10 m. What is AD, in meters?

2018 April(A09) Math Question 24

2019 April(Z15) Math Question 24

2019 April(Z15) Math Question 26

27. All of the following statements concern triangles that are similar, congruent, or both. Which statement is FALSE ?

2014 April(71H) Math Question 27

2010 June(68C) Math Question 27

28. Jamie claims, "If a triangle is in Set A, then it is not isosceles." Later, Jamie discovers that AMNP is a counterexample proving this claim false. Which of the following statements must be true about AMNP ?

2017 June(74C) Math Question 28

2010 December(69A) Math Question 28

2010 April(68G) Math Question 28

2009 April(66F) Math Question 28

30. What is the perimeter, in inches, of the isosceles right triangle shown below, whose hypotenuse is 8√2 inches

2014 June(72C) Math Question 30

2019 June(72F) Math Question 30

2009 December(68A) Math Question 31

32. In isosceles triangle PQR shown below, PQ = QR and the measure of P is 54°. If it can be determined, what is the measure of Q ?

2015 December(72E) Math Question 32

The angle-angle-side (AAS) congruence postulate can be used to prove △JKL ≅ △NOP using only 3 congruence statements. Given the 2 statements KL ≅ OP and ∠L ≅ ∠P, which of the following is the third congruence statement for AAS?

2026 April(R4A) Math Question 32

An isosceles triangle, △ABC, with AB ≅ CB is shown. Points D, E, and H are the midpoints of AB, CB, and AC, respectively. Points F and G are the midpoints of DH and EH, respectively. What is the ratio of the area of △ABC to the area of △FGH?

2025 October(J08) Math Question 34

35. Shown below are right triangles ACD and ABE with lengths given in inches. What is the length, in inches, of AB ?

2014 December(72G) Math Question 35

2012 April(70G) Math Question 35

2009 December(68A) Math Question 36

37. In the figure shown below, LABC ADEF, sides AB and BC are each 7.2 cm long, side DE is 10.8 cm long, and the measure of LE is 42°. What is the measure of C?

2016 April(73E) Math Question 37

38. Shown in the standard (x,y) coordinate plane below is equilateral triangle A0C with coordinates A(a,b), C(4c,0), and O(0,0). In terms of c, what is a ?

2015 April(73G) Math Question 38

2013 December(71E) Math Question 40

2010 June(68C) Math Question 40

40. Equilateral triangle △ABC is shown below with each side length given in meters. What is the value of k ?

2014 April(71H) Math Question 40

2018 December(B05) Math Question 40

2013 December(71E) Math Question 41

2013 April(71G) Math Question 43

44. The points E(6,4) and F(14,12) lie in the standard (x,y) coordinate plane shown below. Point D lies on EF between E and F such that the length of EF is 4 times the length of DE. What are the coordinates of D ?

2014 June(72C) Math Question 44

2009 April(66F) Math Question 44

2012 December(71A) Math Question 47

48. The side lengths of a certain triangle are 4, 5, and 7 centimeters. Which of the following descriptions best classifies this triangle?

2017 June(74C) Math Question 48

48. In AACD shown below, BE is parallel to CD; and the given lengths are in feet. Given that CD denotes the length, in feet, of CD, which of the following proportions involving CD must be true?

2013 June(71C) Math Question 48

The 2 circles graphed in the standard (x,y) coordinate plane below are centered at the origin, O. In coordinate units, the radius of the smaller circle is 2, and the radius of the larger circle is 4. Points A(−4,0), B, and C(4,0) are on the larger circle. The measure of ∠BOC is 45°.

2021 June(D06) Math Question 48

51. The 3 lines with equations y = 4, x = —3, and y = x, respectively, bound a unique triangular region in the standard (x,y) coordinate plane. Which of the following descriptions is the best classification of this triangle?

2016 December(74H) Math Question 51

51. In the standard (x,y) coordinate plane below, point A has coordinates (2,−4), and point B(8,−1) divides AC ___ so that the ratio AB:BC is 1:3. What are the coordinates of point C ?

2021 December(E23) Math Question 51

52. Which of the following sets of 3 lengths, in decimeters, are the side lengths of an obtuse triangle? (Note: An obtuse triangle has 1 angle whose measure is greater than 90° and less than 180°.)

Similar Triangles & Types of TrianglesThere are 56 ACT math questions under Similar Triangles & Types of Triangles

Sub-topics

2018 December(B05) Math Question 2

2019 April(Z15) Math Question 3