Question

rhombus.
Ota
[CBSE 2015]
18
13. In the given figure, in A ABC, D and E are
the mid-points of the sides BC and AC
respectively. Find the length of DE. Prove
2
1
that DE-AB.
[HOTS; CBSE 2011) 1
C (-6, -1)
DA
E
2015]
B (2,-2)
A (4,-2)
2013]​

Answer 1

Explanation:

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,

Area(△ABC)

Area(△ADE)

=

AB

2

AD

2

(Similar triangle property)

Area(△ABC)

Area(△ADE)

=

(2AD)

2

AD

2

Area(△ABC)

Area(△ADE)

=1:4