PRINCIPIA · THEOREM

Isoceles trapezoid: diagonals equal

Dependencies: SAS congruence, Isoceles trapezoid: base angles equal.

Statement

Let $ABCD$ be an isosceles trapezoid, where $AD \parallel BC$ are the two bases (we take $AD$ to be the upper base and $BC$ the lower base) and $AB$ , $DC$ are the two equal legs:

AD \parallel BC,\qquad AB = DC.

Then the two diagonals are equal in length:

AC = BD.

$Isosceles trapezoid ABCD (AD \parallel BC, AB = DC): the two diagonals satisfy AC = BD.$

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