properties of parallelograms objective: to use relationships among sides, angles, diagonals or...
TRANSCRIPT
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Properties of Parallelograms
Objective: To use relationships among sides, angles, diagonals or
transversals of parallelograms.
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Summary of Properties
• Opposite sides are parallel• Opposite sides are equal• Opposite angles are equal• Consecutive angles are supplementary• diagonals bisect each other (cut each other in
half)
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Practice
• The opposite sides of a parallelogram areRepresented by 2x+10 and5x-20. Find the length of theParallelogram represented By 4x-1.
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Use KMOQ to find m O.
Q and O are consecutive angles of KMOQ, so they are supplementary.
Definition of supplementary anglesm O + m Q = 180
Substitute 35 for m Q.m O + 35 = 180
Subtract 35 from each side.m O = 145
Properties of Parallelograms
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Find the value of x in ABCD. Then find m A.
2x + 15 = 135 Add x to each side.
2x = 120 Subtract 15 from each side.
x = 60 Divide each side by 2.
x + 15 = 135 – x Opposite angles of a are congruent.
Substitute 60 for x. m B = 60 + 15 = 75
Consecutive angles of a parallelogram are supplementary.
m A + m B = 180
Subtract 75 from each side.m A = 105
m A + 75 = 180 Substitute 75 for m B.
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Using Algebra
• Find the value of y in EFGH. Then find m<E, m<F, m<G, m<H.
E F
GH
3y + 37
6y + 4
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Example
3y-7
X+1 y
2x