PRINCIPIA · THEOREM

Isoceles trapezoid: diagonals equal

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

Statement

Let ABCDABCD be an isosceles trapezoid, where AD∥BCAD \parallel BC are the two bases (we take ADAD to be the upper base and BCBC the lower base) and ABAB, DCDC are the two equal legs:

AD∥BC,AB=DC.AD \parallel BC,\qquad AB = DC.

Then the two diagonals are equal in length:

AC=BD.AC = BD.

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

10 foundational theorems free · one-time unlock for the rest

Unlock the complete proofs forever

Matching GeoSnap, 10 foundational theorems are completely free. Unlock every other proof, animation, and consequence with one $10 purchase.

Sign in to unlock
Help me make this theorem better