Question

In triangle ABC, D and E are mid points of AB and AC respectively. Find area 4 ABC: area 4 ADE.

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Answer 1

Step-by-step explanation:

Given: D and E are mid points of AB and AC

By mid point theorem, DE∥BC

In △ADE and △ABC

∠DAE=∠BAC (Common)

∠ADE=∠ABC (Corresponding angles)

∠AED=∠ACB (Corresponding angles)

Thus, △ABC∼△ADE (AAA rule)

Hence,

A(△ABC)

A(△ADE)

=

AB

2

AD

2

(Similar triangle property)

A(△ABC)

A(△ADE)

=

(2AD)

2

AD

2

A(△ABC)

A(△ADE)

=1:4

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