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

1 Answer
Nov 21, 2015

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#.