Question

(c) If the non-parallel sides AD and BC of the trapezium ABCD are equal then prove that D equal to C and A equal to B.

Answer 1

Answer:

Join CE and produce it to meet BA produced at G

In △EDC and △EAG,

⇒ ∠CED=∠GEA [ Vertically opposite angles ]

⇒ ∠ECD=∠EGA [ Alternate angles ]

⇒ ED=EA [ Since, E is the midpoint of AD ]

⇒ △EDC≅△EAG [ By AAS congruence theorem ]

⇒ CD=GA and EC=EG [ By CPCT ]

In △CGB,

E is the midpoint of CG and F is the mid-point of BC.

By mid-point theorem,

∴ EF∥AB

Hence Proved.

solution