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

Triangles Hard

CD and GH are respectively the bisectors of

∠ A C B

and

∠ E GF

such that D and H lie on sides AB and FE of

△ A B C

and

△ E F G

respectively. If

△ A B C \sim △ F E G

, show that:

Answer

Using

△ A B C \sim △ F E G

and the equal half-angles from the bisectors, the AA criterion gives

△ D C B \sim △ H GE

and

△ D C A \sim △ H GF

; the side ratio of the latter yields

\frac{C D}{G H} = \frac{A C}{F G}

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