Proving the Single Opposite Side Pair Theorem

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+Given: AD - BC and AD || BC

Prove: ABCD is a parallelogram.

Angles Segments Triangles Statements Reasons

ABCD is a parallelogram

ZDAC and BCA

are alt interior angles

A

B

Statements

V 1. AD BC

2. AD || BC

3. ACAC

4. ZDAC and BCA

are alt interior angles

5. ZBCA Z DAC

Reasons

1 given

2. Given

3. Reflexive property

4. Def. Of alt, interior angles

D

C

5. Alternate interior angles theorem

Hint

Intro