# In Fig. 6.37, if Δ ABE ≅Δ ACD, show thatΔ ADE ~ Δ ABC.

To Prove: Δ  ADE ∼ Δ ABC

Given: ΔABE ΔACD

Proof:

ΔABE ≅ ΔACD

AB = AC                     (By CPCT) (i)

And,

AD = AE                       (By CPCT) (ii)

Dividing equation (ii) by (i)

A = A (Common)

SAS Similarity: Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal.

Therefore,

Hence, Proved.

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