The shapes are drawn on a square grid. In which pair are the two figures similar?

Class 10Triangles (Similarity)Geometry — Similarity

APair A
BPair B
CPair C
DPair D

Step-by-Step Solution

Similar figures have equal angles and sides in the same ratio. Pair A is two squares

(2 : 2

and

3 : 3

), and all squares are similar. In B the ratios

4 : 2

and

3 : 2

differ, in C the rhombus has

6 0^{\circ}

angles, and in D

4 : 2 \neq = 6 : 4

Answer: A) Pair A

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

k

:
- Corresponding sides differ by factor

k

.
- Corresponding angles are equal (always, by definition).
- Areas differ by factor

k^{2}

— 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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