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Given: Rectangle ABCD Prove: diagonal AC is congruent to diagonal BD?

1 Answer

Nov 21, 2015

See the proof below

Explanation:

Since $A B C D$ $ABCD$ is rectangle, the following relationships of congruence are true:

$A B ≅ C D$ $AB~=CD$
$A D ≅ B C$ $AD~=BC$
$∠ A B C ≅ ∠ B C D ≅ ∠ C D A ≅ ∠ D A B = 90^{o}$ $/_ABC~=/_BCD~=/_CDA~=/_DAB=90^o$

Therefore, $Delta ABC ~= Delta ABD$ 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 $BD$ .

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