Question

in figure line segment DF intersects the side AC of a triangle ABC at the point is such that is the midpoint of AC and Angle A e f is equal to angle A if P then prove that BD by CD is equal to BF by CE​

Answer 1

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Solution:-

Given :-

/_ AEF = /_ AFE

=> AF = AE________(1)

AE = CE ( E is the mid point)_______(2)

From Eq 1 & 2. we get,

AE = CE = AF ________(3).

Construction :- Draw a line segment CZ || EF.

=> By BPT,

AF / GF = AE / EC ________(4).

Since, CZ || EF

=> CZ || DF ( EF is extended to D)

By BPT,

BC / CD = BZ / ZF

=> BC / CD = BZ / ZF

Adding 1 on both the sides. we get,

BC / CD + 1 = BZ/ ZF +1

=> BC + CD / CD = BZ + ZF / ZF

=> BD / CD = BF / ZF

=> BD / CD = BF / CE ( ZF = CE).

Hence Proved.

Answer 2

Answer:

Step-by-step explanation: