Class 10 Triangles (Similarity) — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Two triangles have angles 30°, 60°, and 90°. Are they similar?
AYes, by AA criterion
BNo, angles are not enough
CYes, by SSS criterion
DNo, they must be congruent
Show answer
Answer: A) Yes, by AA criterion
Triangles with two equal angles are similar by the AA criterion.
2. State the Basic Proportionality Theorem (Thales' Theorem).
AIf a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, the other two sides are divided in the same ratio.
BThe sum of the angles of a triangle is 180 degrees.
CIn a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
DThe ratio of areas of similar triangles equals the ratio of their sides.
Show answer
Answer: A) If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, the other two sides are divided in the same ratio.
The Basic Proportionality Theorem (BPT), also called Thales' Theorem, states exactly this: a line parallel to one side divides the other two sides in the same ratio.
3. In triangle ABC, the bisector of angle A meets BC at D. If AB = 6 cm, AC = 9 cm and BC = 10 cm, find BD (in cm).
A4
B5
C8
D3
Show answer
Answer: A) 4
By the Angle Bisector Theorem, DCBD=ACAB=96=32. So BD = 52 * 10 = 4 cm.
4. Triangle ABC ~ Triangle PQR with PQAB=52. If the area of triangle PQR is 100 cm², find the area of triangle ABC (in cm²).
A17
B15
C32
D16
Show answer
Answer: D) 16
Area ratio = (52)2=254. Area of ABC = 100 * 254 = 16 cm².
5. A girl of height 90 cm walks away from the base of a lamp-post 3.6 m high at a speed of 1.2 m/s. After 4 seconds, find the length of her shadow (in m).
A3.2
B1.6
C1.1
D2.1
Show answer
Answer: B) 1.6
Lamp height 3.6 m, girl height 0.9 m. By similar triangles, shadow length s satisfies 3.60.9=distance walked+ss. After 4 s she walks 1.2*4 = 4.8 m. So 3.60.9=4.8+ss, i.e. 41=4.8+ss. Then 4.8 + s = 4s, so 3s = 4.8, s = 1.6 m.