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Mathematics

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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 :

HABONU514315GO HABONU514315GO

The Solution:

Required:

To prove that opposite sides are congruent in a parallelogram.

Step 1:

Draw a parallelogram.

Step 2:

[tex]DB\cong DB\text{ \lparen Reason: Reflexive property\rparen}[/tex]

Step 3:

[tex]AB\parallel CD\text{ and BC }\parallel AD\text{ \lparen Reason: Definition of a parallelogram\rparen}[/tex]

Step 4:

[tex]\angle1\cong\angle4\text{ and }\angle2\cong\angle3\text{ \lparen Reason: Alternative angles are equal.\rparen}[/tex]

Step 5:

[tex]\angle ABD\cong\angle CDB\text{ \lparen Reason: Angle-Side-Angle \lparen ASA\rparen Theorem\rparen}[/tex]

Step 6:

[tex]undefined[/tex]

View image HABONU514315

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