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