Question

prove that diagonal of a square are equal

Answer 1

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(draw a square ABCD with diagonals AC and BD)Given:ABCD is a square
To prove:AC=BD and AC and BD bisect each other at right. angles

Proof:In triangle ACB and triangle BAD

AB=AB (common side)
angle ABC=angle BAD(=90degree)
BC=AD(opposite sides of a square)

Triangle ACB congruent BAD(SAS criteria)
AC=BD by(CPCT)

in triangle OAD and OBC

angle OAB=OCB(AC transversal)
AD=CB(opposite sides of square)
angle ODA=OBC(BD transversal)

OA=OC

Answer 2

Given :- ABCD is a square.

To proof :- AC = BD and AC ⊥ BD

Proof :- In △ ADB and △ BCA

AD = BC [ Sides of a square are equal ]

∠BAD = ∠ABC [ 90° each ]

AB = BA [ Common side ]

△ADB ≅ △BCA [ SAS congruency rule ]

⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]