Class 10 Criteria for Similarity — practice questions with answers
Geometry — Similarity · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which criterion proves two triangles similar if two angles of one equal two angles of the other?
AAA criterion
BSSS criterion
CSAS criterion
DRHS criterion
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Answer: A) AA criterion
If two pairs of corresponding angles are equal, the triangles are similar by the AA (Angle-Angle) criterion.
2. In the figure, DE is parallel to BC. Which criterion proves triangle ADE ~ triangle ABC?
AAA
BSSS
CSAS
DRHS
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Answer: A) AA
DE || BC gives angle ADE = angle ABC and angle AED = angle ACB (corresponding angles); angle A common. Two angles equal means AA.
3. Triangle ABC ~ triangle DEF. If BC = 5 cm, EF = 10 cm and the perimeter of triangle DEF is 40 cm, the perimeter of triangle ABC is:
A22
B40
C20
D18
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Answer: C) 20
EFBC=105=21 = perimeter ratio. So perimeter ABC = 40 x 1/2 = 20 cm.
4. Triangle ABC ~ triangle PQR. The ratio of their areas is 9:25. If BC = 12 cm, find QR (in cm).
A20
B22
C40
D18
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Answer: A) 20
Ratio of areas = (side ratio)² = 259, so side ratio = 53. QRBC=53, QR12=53, QR = 20 cm.
5. Two poles of heights 6 m and 11 m stand vertically on the ground with feet 12 m apart. Wires are drawn from the top of each pole to the foot of the other; they cross at point P. Using the similar triangles formed, the height of P above the ground (in m) is:
A2.88
B4.88
C3.88
D7.76
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Answer: C) 3.88
Height of crossing of two such 'X' wires = (h1 x h2)/(h1+h2) = (6 x 11)/(6+11) = 66/17 = 3.88 m (approx).