Class 9 Criteria for Congruence — practice questions with answers
Geometry — Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which rule states that two triangles are congruent if all three sides of one equal all three sides of the other?
ASSS
BSAS
CASA
DRHS
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Answer: A) SSS
Side-Side-Side (SSS): if the three sides of one triangle equal the three sides of another, the triangles are congruent.
2. Triangle ABC is congruent to triangle DEF with AB = 5 cm. The length of side DE is:
A4
B10
C5
D6
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Answer: C) 5
By CPCT, DE corresponds to AB, so DE = 5 cm.
3. Which criterion uses the Pythagoras relationship implicitly to justify it?
ARHS
BASA
CSSS
DAAS
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Answer: A) RHS
Given the hypotenuse and one leg, Pythagoras fixes the third side, making RHS equivalent to SSS.
4. In triangle ABC, AB = AC. The perpendiculars BE and CF are drawn to sides AC and AB respectively. To prove BE = CF using triangles ABE and ACF, the criterion is (angle A common, right angles equal, AB=AC):
AAAS
BSSS
CSAS
DRHS
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Answer: A) AAS
angle A is common, angle AEB = angle AFC = 90 deg, and AB = AC (non-included side). Two angles + a side => AAS.
5. In triangle ABC, points D on AB and E on AC satisfy AD = AE and BD = CE. Prove triangle ABE is congruent to triangle ACD by first noting AB = AD + DB and AC = AE + EC. Which equality of full sides follows?
AAB = AC
BAD = DB
CBD = AE
DAB = AE
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Answer: A) AB = AC
AB = AD + DB and AC = AE + EC; since AD = AE and DB = EC, we get AB = AC. With common angle A, SAS then gives congruence.