P and Q are the midpoints of the non-parallel sides AB and CD in a trapezium. AD = 24 cm and PQ = 20 cm. Calculate the length of the other parallel side of the trapezium
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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.
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MARK AS A BRANALIST
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