Question

21 pointUse the given information to complete the proof of the following theorem.If a quadrilateral is a parallelogram, then its opposite sides are congruent.By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.angle-side-angleCorresponding parts of congruent triangles are congruent.side-angle-sideOpposite sides of a parallelogram are congruent.

Answer 1

The Solution:

Required:

To prove that opposite sides are congruent in a parallelogram.

Step 1:

Draw a parallelogram.

Step 2:

`DB\cong DB\text{ \lparen Reason: Reflexive property\rparen}`

Step 3:

Step 4:

`\angle1\cong\angle4\text{ and }\angle2\cong\angle3\text{ \lparen Reason: Alternative angles are equal.\rparen}`

Step 5:

`\angle ABD\cong\angle CDB\text{ \lparen Reason: Angle-Side-Angle \lparen ASA\rparen Theorem\rparen}`

Step 6: