- A13.5 cm
- B8 cm
- C6 cm
- D4.5 cm
Step-by-Step Solution
Alternate angles give Δ ~ Δ, so , i.e. , giving cm. 13.5 cm comes from inverting the ratio ; 8 cm is simply copying ; 4.5 cm is halving .
Answer: C) 6 cm
In trapezium PQRS, PQ ∥ SR and the diagonals meet at O. If PQ = 12 cm, SR = 8 cm and OQ = 9 cm, find OS.
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Similarity vs congruence
**Congruent**: same shape AND same size. All corresponding parts equal.
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).
If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.
**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).
If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.
**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).
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