Class 10 Maths · Triangles · NCERT Exercise 6.4 · Question 16

Triangles Hard

In Fig. 6.22, line segment DF intersects the side AC of a triangle ABC at the point E such that E is the mid-point of CA and

∠ A E F = ∠ A F E

. Prove that

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

. [Hint: Take point G on AB such that CG

∥

DF.]

Fig. 6.22

Answer

Proved: with

C G ∥ D F

, BPT gives

\frac{B D}{D C} = \frac{B F}{F G}

, and since

F G = A F = A E = E C

, we get

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

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