Question

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

Answer 1

See the proof below

Explanation:

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

`AB~=CD`
`AD~=BC`
`/_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`.