6.2 Properties of Parallelograms
• A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
• In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.
Theorem 6.3
• If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Consecutive Angles
• Angles of a polygon that share a side are consecutive angles.
Theorem 6.4
• If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Using Consecutive Angles
• What is the measure of angle P in parallelogram PQRS?
A. 26°B. 64°C. 116°D. 126°
180m P m S
64 180m P
116m P
Theorem 6.5
• If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Theorem 6.6
• If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Using Algebra to Find Lengths
• Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?
Using Algebra to Find LengthsKP MP
LP NP10 2 8y x
2x y 10 2( 2) 8y y 10 2 4 8y y 10 4y 14 y14 2x 16x
2( )KM KP2( 10)KM y 2(14 10) 48
2( )LN LP2LN x2(16)32
Theorem 6.7
• If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Using Parallel Lines and Transversals
• In the figure, AE || BF || CG || DH, AB = BC = CD = 2, and EF = 2.25. What is EH?
EF = FG = GH
EH = EF + FG + GH
EH = 2.25 + 2.25 + 2.25
EH = 6.75
More Practice!!!!!
• Homework – p. 364 - 365 #9 – 12, 14 – 27, 29 – 30 ALL.
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