Question

In a rectangle ABCD prove that AC=BD

Answer 1

Since ABCD is rectangle, the following relationships of congruence are true:

AB≅CD
AD≅BC
∠ABC≅∠BCD≅∠CDA≅∠DAB=90o

Therefore, ΔABC≅ΔABD as right triangles with congruent catheti BC and AD and shared cathetus AB.

From congruence of these triangles follow the congruence of their hypotenuses AC and BD

Answer 2

Hi friend
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Your answer
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To prove : - AC = BD

In rectangle ABCD,
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In ∆ ABC and ∆ ADB ,we have,

BC = AD (opposite sides of a rectangle are equal)

AB = AB (common(

angle ABC = angle DAB (90° each)

Therefore, ∆ABC is congruent to ∆ ADB . (By SAS congruency)

So,

AC = BD ( By CPCT)

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