Question

In the adjoining figure, angle BAC = angle BDC and angle ABC = angleBCD. Prove that! (1) Triangle ABC congruent Triangle DCB (ii) Triangle Abe congruence DCF

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Answer 1

Answer:

Given : ΔFECΔFEC≅ΔGDB

EC=BD (by CPCT ) ...(1)

Given ∠1=∠2

AEAD ...(2)

(Sides opposite to equal angles are equal)

From eq 1 and 2

AE/EC=AD/BAD

DE∣∣BC (Converse of Basic Proportionality Theorem)

∠1=∠3 and ∠2=∠4 [Correspoding angles]

In ΔADE and ΔABC

∠A=∠A..(Common)

∠1=∠3.(proved above)

∠2=∠4 ..(proved above)

ΔADE∼ΔABC..[by AAA similarity criterion]

Step-by-step explanation:

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