Question

Drag and drop an answer to each box to correctly complete the proof.


Given: Parallelogram JKLM is a rectangle.


Prove: JL¯¯¯¯¯≅MK¯¯¯¯¯¯¯

Answer 1

Answer:

1. all the right angles are congruent

2. opposite sides of a parallelogram are congruent

3. SAS congruent postulate

4. corresponding parts of a congruent triangle are congruent

Step-by-step explanation:

1. As all the right angles are congruent

          ∠JML≅∠KLM≅ ∠90°

2. As per the properties of a parallelogram, the opposite sides are congruent.

                  Hence the sides JM≅KL

3. SAS postulate is defined as Side-Angle-Side postulate. When the side, adjacent angle and the other other adjacent side of two triangle are congruent then the two triangles are said to be congruent. In the given case both the sides JM and ML of ΔJML are congruent to both the sides KL and ML of ΔKLM.

                            Hence ΔJML≅ΔKLM

4. As proven in part 3, ΔJML≅ΔKLM so the congruent parts of two congruent triangle are congruent.

                In given case the side JL(of ΔJML)≅MK(ΔKLM)

!

Answer 2

The completed proof is presented as follows;

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, $\overline{JM}$ ≅ $\overline{KL}$ because opposite sides of a parallelogram are

congruent, and $\overline{ML}$ ≅ $\overline{ML}$ by reflective property of congruence. By the SAS

congruence postulate, ΔJML ≅ ΔKLM. Because, congruent parts of

congruent triangles are congruent, $\overline{JL}$ ≅ $\overline{MK}$

Reasons:

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

parallelogram including;

• The length of opposite sides are equal

All right angles are congruent and equal to 90°

The length of a side is equal to itself by reflexive property, therefore,  $\overline{ML}$

≅ $\overline{ML}$

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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