Properties

of a

Parallelogram Summary A parallelogram is a quadrilateral with two pairs of parallel sides Proof:

Statements Reasons

1. JKLM is a parallelogram 1. Given

2. JK || LM, KL || MJ 2. Definition of a parallelogram

3. Angle 1 is congruent to angle 2 3. Alternant Interior Angle

Angle 3 is congruent to angle 4

4. JL is congruent to JL 4. Reflexive Property

5. Triangle JKL is congruent 5. ASA

to triangle LMJ

6. JK is congruent to LM, 6. CPCTC

KL is congruent to MJ

Theorem 1: If a quadrilateral is a parallelogram, then its opposite sides are congruent. Proof:

Statements Reasons

1. ABCD is a parallelogram 1. Given

2. AB is congruent to CD, 2. Opposite sides of a parallelogram are

DA is congruent to BC congruent

3. BD is congruent to BD 3. Reflexive

4. Triangle BAD is congruent 4. SSS

to triangle DCB

5. Angle BAD is congruent 5. CPCTC

to Angle DCB

6. AC is congruent toAC 6. Reflexive

7. Triangle ABC is congruent 7. SSS

to triangle CDA

8. Angle ABC is congruent 8. CPCTC

to Angle CDA Theorem 2: If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem 3: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. A parallelogram has 2 pairs of parallel sides

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonols bisect each other Theorem 4: If a quadrilateral is a parallelogram, then its diagonals bisect each other.

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# Properties of a Parallelogram

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