CBSE Class 10 Maths (Standard) 2024 · Paper 30/5/1 · Question 34(a)

Triangles 5 marks Medium

In the given figure,

△ F E C ≅ △ G D B

and

∠1 = ∠2

. Prove that

△ A D E \sim △ A B C

Answer

Since

∠1 = ∠2

A D = A E

; by CPCT from

△ F E C ≅ △ G D B

E C = D B

. So

\frac{A D}{D B} = \frac{A E}{E C}

and

D E ∥ B C

(converse of BPT), giving

∠ A D E = ∠ A B C

. With

∠ A

common,

△ A D E \sim △ A B C

(AA). Hence proved.

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