Class 9 SSS and RHS 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. What does the SSS congruence rule stand for?
- ASide-Side-Side
- BSide-Angle-Side
- CSide-Side-Angle
- DSide-Angle-Angle
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Answer: A) Side-Side-Side
SSS stands for Side-Side-Side: two triangles are congruent if all three sides of one equal the corresponding three sides of the other.
2. Two right triangles each have hypotenuse 13 cm and one leg 5 cm. The other leg of each is (in cm):
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Answer: C) 12
Other leg =
132−52 =
169−25 =
144 = 12 cm. By RHS both triangles are congruent.
3. Rahul draws a triangle with sides 8 cm, 8 cm, 8 cm. Priya draws one with sides 8 cm, 8 cm, 9 cm. Are the triangles congruent?
- ANo, third sides differ
- BYes, by SSS
- CYes, by RHS
- DYes, by AAA
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Answer: A) No, third sides differ
Two sides match but the third (8 vs 9) differs, so SSS fails; the triangles are not congruent.
4. Two triangles have sides {a, b, c} and {a, b, c} but one is the mirror image (flipped) of the other.
Are they still congruent under SSS?
- AYes, congruence allows reflections
- BNo, mirror images are never congruent
- COnly if the triangle is equilateral
- DOnly if a = b = c
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Answer: A) Yes, congruence allows reflections
Congruence permits rigid motions including reflection. Equal three sides still give SSS congruence even if one is flipped.
5. Two triangular tiles have sides {x, x+2, x+4} and {7, 9, 11} respectively and are congruent by SSS.
Find the value of x.
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Answer: A) 7
Matching smallest to smallest: x = 7, x+2 = 9, x+4 = 11. All consistent, so x = 7.