Question

please give this answer​

Answer 1

Solution :-

In ΔCAB,

CD/DA = CE / EB [ Given ]

Therefore,

DE parallel to AB

[ If a line divides any two sides of a triangle in the same ratio, then the line is parallel to third side ]

ΔCDE = ΔCAB

[ Corresponding angles ]( 1 )

ΔCED = ΔCBA

[ Corresponding angles ] ( 2 )

ΔCDE = ΔCED.

[ Given ] ( 3 )

Therefore ,

From ( 1 ) , ( 2 ) and ( 3 )

ΔCAB = ΔCBA

CB = CA [ Converse of isosceles triangle ]

Therefore,

ΔCAB is an isosceles triangle.

Theorem kept in Mind :-

• If a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

[ This theorem is called Basic proportionality Theorem ]

• If a line divides any two sides of triangle in the same ratio, then the line is parallel to third side.

[ This Theorem is called Converse of basic proportionality Theorem ]