Question

Suppose in a quadrilateral $$ABCD, AD = BC$$ and $$AC = BD$$. Prove that $$ABCD$$ is a trapezium.

Solution

Given: $$ABCD$$ is a quadrilateral,$$AC = BD$$ and $$AD = BC$$To prove: $$ABCD$$ is trapeziumProof: In $$Δ ADB$$ and $$Δ BCA$$(1) $$AD = BC$$ (Given)(2) $$AC = BD$$ (Given)(3) $$AB = AB$$ (Common side)$$∴ Δ ADB ≅ Δ BCA$$ (SSS postulate)$$∴ ∠A = ∠B$$ (Congruency property)$$AC = BD$$ (Given), $$AD = BC$$ (Given)Hence, $$ABCD$$ is an isosceles trapezium.Mathematics

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