CBSE Class 10 Maths (Standard) 2020 · Paper 30/1/1 · Question 31

Triangles 3 marks Medium

In Fig. 5,

∠ D = ∠ E

and

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

, prove that

△ B A C

is an isosceles triangle.

Fig. 5

Answer

Since

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

gives

D E ∥ B C

, the corresponding angles make

∠ A B C = ∠ A C B

(using

∠ A D E = ∠ A E D

); hence

A B = A C

and

△ B A C

is isosceles. Q.E.D.

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