1. Two figures that have the same shape and the same size are said to be:
- ASimilar
- BCongruent
- CSymmetric
- DParallel
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Answer: B) Congruent
Same shape AND same size means congruent. Same shape but possibly different size means similar.
Class 10 Similarity and Congruence — practice questions with answers
Geometry — Similarity · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. In triangle ABC ~ triangle PQR, angle A = 50 deg and angle B = 60 deg. Find angle R (in degrees).
- A77
- B70
- C140
- D63
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Answer: B) 70
angle C = 180 - 50 - 60 = 70 deg. Since the triangles are similar, angle R = angle C = 70 deg.
3. The symbol used to denote 'is similar to' is:
- A=
- B~
- C≅
- D||
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Answer: B) ~
The tilde symbol ~ means 'is similar to'; the symbol with a tilde over an equals sign means 'is congruent to'.
4. Statement P: Two equilateral triangles are always similar.
Statement Q: Two equilateral triangles are always congruent.
Which is correct?
Statement Q: Two equilateral triangles are always congruent.
Which is correct?
- ABoth P and Q are true
- BP is true, Q is false
- CP is false, Q is true
- DBoth are false
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Answer: B) P is true, Q is false
All equilateral triangles share 60 deg angles so they are similar (P true). Sizes may differ, so they need not be congruent (Q false).
5. A rangoli design is made of two similar triangles. The larger triangle has each side 1.5 times the corresponding side of the smaller one, and uses 360 cm² of coloured powder (proportional to area). The smaller triangle uses x cm² of powder.
Find x (in cm²).
Find x (in cm²).
- A160
- B320
- C175
- D145
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Answer: A) 160
Area ratio (large:small) = 1.5² = 2.25. So 360/x = 2.25, giving x = 360/2.25 = 160 cm².
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