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Tests for Congruency of Triangles

8. Prove that...

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8. Prove that area of triangle ACE is equal to 1/4 area ABC.If E is the mid point of median AD of triangle ABC

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Q. In a triangle ABC, E is the midpoint of median AD, show that

a r e a △ A B E = a r e a △ A C E

Q. In a triangle

A B C, E

is the mid-point of median

A D

a r e a (B E D) = \frac{1}{4} a r e a (A B C)

Q. If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in area. If G is the mid-point of median AD, prove that ar(Δ BGC)= 2 ar (Δ AGC).

A B C

A D

C E

A D = 5

∠ D A C = π / 8

∠ A C E = π / 4

, then the area of the triangle

A B C

Q. In given figure,

E

is any point on median

A D

△ A B C

a r e a (A B E) = a r e a (A C E)

.

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Tests for Congruency of Triangles

Standard IX Mathematics

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