Question

AD and PS are angle bisectors of $∠ A$ and $∠ P$ of triangles ABC and PQR. If $△ A BC \sim △ PQR$ , prove that $△ A C D \sim △ PRS$ .

Approach

Since $△ A BC \sim △ PQR$ , corresponding angles are equal. AD and PS are angle bisectors, so $∠ C A D = \frac{1}{2} ∠ A = \frac{1}{2} ∠ P = ∠ RPS$ . Also $∠ C = ∠ R$ . By AA criterion, $△ A C D \sim △ PRS$ .

Step-by-step working

1
Given: $△ A BC \sim △ PQR$ and AD, PS are angle bisectors
1 mark
2
By AA similarity, $△ A C D \sim △ PRS$
1 mark

Concepts used

similarityangle bisectortrianglesproof

Approach

Step-by-step working

Concepts used

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