If the diagonals of a parallelogram are equal, then show that it is a rectangle
If the diagonals of a parallelogram are equal, then show that it is a rectangle

Question: Abigail wants to prove that a parallelogram is a rectangle if its diagonals are congruent. To start her proof, she draws parallelogram JKLM with congruent diagonals overline JL and overline KM. Complete the proof that JKLM is a rectangle. Since JKLM is a parallelogram, overline JK ≌ overline ML . Also, by the _ overline KL is congruent to itself. So, since overline JL ≌ overline KM as well, by the _ Congruence Theorem. _ Now, because are congruent, angle JKL ≌ angle MLK. _ Also, since parallelograms have . So, since mangle JKL and mangle MLK are equal, they must both be _ 90 ° . Because are congruent, mangle MJK and mangle JML are _ also both 90 ° . So, parallelogram JKLM is a rectangle because it has four right angles. _

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