Class 10 Maths · Triangles · NCERT Exercise 6.3 · Question 11

Triangles Medium

In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with

A B = A C

. If

A D ⊥ B C

and

E F ⊥ A C

, prove that

△ A B D \sim △ E C F

Fig. 6.40

Answer

△ A B D

and

△ E C F

we have

∠ A D B = ∠ E F C = 9 0^{\circ}

(from

A D ⊥ B C

and

E F ⊥ A C

) and

∠ A B D = ∠ E C F

(each equals a base angle of the isosceles triangle, since

A B = A C

). Hence, by the AA similarity criterion,

△ A B D \sim △ E C F

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