Question

prove that the diagonals of an isoceles trapezoid are equal

Answer 1

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Consider the isosceles trapezium trapezoid ABCD, where:

• AD || BC

• AB = CD

• ∠BAD = ∠CDA (a given condition ∵ ABCD is an isosceles trapezium)

The diagonals AC and BD create two ∆'s: ∆ABD, and ∆ACD

The two ∆'s are congruent (SAS).

Justification?

• (S): AB = CD

• (A): ∠BAD = ∠CDA

• (S): AD = DA (common side)

∴ the corresponding sides of the two ∆'s, BD and AC, are also congruent.

(the two diagonals of the trapezium/trapezoid, as required.

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