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Given: rectangle JKLM

prove: JL = MK

2 Answers

12 votes

Answer:

(In order, top to bottom. )

Definition of a rectangle

opposite sides of a rectangle are congruent

reflexive property of congruence

SAS congruence postulate

Explanation:

Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML

and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are

congruent, ≅ because opposite sides of a parallelogram are congruent, and ≅ by reflective property of congruence. By the SAS

congruence postulate, ΔJML ≅ ΔKLM.

congruent parts of congruent triangles are congruent, ≅

The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and

parallelograms including the length of opposite sides are equal, all right angles are congruent and equal to 90° and the length of a side is equal to itself by reflexive property, & ≅

The Side-Angle-Side SAS postulate states that if two sides and an included

angle of one triangle are congruent to the corresponding two of sides and

included angle of another triangle, the two triangles are congruent.

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