Online Test — Triangles
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
If two triangles are similar, their corresponding sides are always...
Equal
Proportional
Perpendicular
Parallel
Explanation: Similar figures have proportional side lengths by definition.
Question 2 of 10
medium
Which of the following is NOT a valid criterion for triangle similarity?
AAA
SAS
SSS
SSA
Explanation: SSA does not guarantee a unique triangle shape.
Question 3 of 10
medium
Triangle ABC ~ Triangle PQR. If AB = 4 cm, PQ = 6 cm, and the perimeter of ABC is 12 cm, what is the perimeter of PQR?
18 cm
16 cm
24 cm
14 cm
Explanation: The perimeter ratio matches the side ratio: 4/6 = 12/x, so x = 18.
Question 4 of 10
medium
A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 40 m long. Find the tower's height.
32 m
50 m
45 m
60 m
Explanation: Ratio: 10/8 = Height/40. Height = 5 * 10 = 50.
Question 5 of 10
medium
Triangle ABC ~ Triangle DEF. If AB/DE = 2/3, what is the ratio of Area(ABC) to Area(DEF)?
2/3
4/6
4/9
8/27
Explanation: Area ratio is the square of the side ratio: (2/3) squared = 4/9.
Question 6 of 10
medium
The areas of two similar triangles are 64 square cm and 121 square cm. What is the ratio of their corresponding heights?
8:11
64:121
16:22
4:5.5
Explanation: Height ratio is the square root of the area ratio: sqrt(64/121) = 8/11.
Question 7 of 10
medium
In a right triangle, if the hypotenuse is 5 cm and the base is 3 cm, what is the vertical height?
2 cm
4 cm
6 cm
16 cm
Explanation: Height = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt(16) = 4.
Question 8 of 10
medium
Which set of side lengths forms a valid right-angled triangle?
2 cm, 3 cm, 4 cm
5 cm, 10 cm, 12 cm
8 cm, 15 cm, 17 cm
6 cm, 8 cm, 11 cm
Explanation: 8^2 + 15^2 = 64 + 225 = 289, which equals 17^2.
Question 9 of 10
medium
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
6 m
14.5 m
sqrt(252) m
sqrt(42) m
Explanation: Distance = sqrt(24^2 - 18^2) = sqrt(576 - 324) = sqrt(252).
Question 10 of 10
medium
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. What is this rule called?
Pythagoras Theorem
Converse of Thales Theorem
Area Theorem
AAA Criterion
Explanation: This describes the Converse of the Basic Proportionality Theorem.