Post on 18-Jan-2016
Bell Ringer
1. 2. 3.
Properties of Parallelograms
Parallelogram
• Parallelogram – is a quadrilateral with both pairs of opposite sides parallel.
Example 1 Find Side Lengths of Parallelograms
FGHJ is a parallelogram. Find JH and FJ.
Substitute 5 for FG.= 5
SOLUTION
JH = FG Opposite sides of a are congruent.
Substitute 3 for GH.= 3
FJ = GH Opposite sides of a are congruent.
ANSWER In FGHJ, JH = 5 and FJ = 3.
Now You Try Find Side Lengths of Parallelograms
ANSWER AB = 9; AD = 8
ABCD is a parallelogram.Find AB and AD.
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Example 2 Find Angle Measures of Parallelograms
PQRS is a parallelogram. Findthe missing angle measures.
SOLUTION
By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mR = mP = 70°.1.
2.By Theorem 6.4, the consecutive angles of a parallelogram are supplementary.
Consecutive angles of a are supplementary.
mQ + mP = 180°
Substitute 70° for mP.mQ + 70° = 180°
Subtract 70° from each side.mQ = 110°
Example 2 Find Angle Measures of Parallelograms
By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mS = mQ = 110°.
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ANSWERThe measure of R is 70°, the measure of Q is 110°, and the measure of S is 110°.
Now You Try Find Angle Measures of Parallelograms
ABCD is a parallelogram. Find the missing angle measures.
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ANSWER
mB = 120°mC = 60°mD = 120°
ANSWER
mA = 75° mB = 105° mC = 75°
Example 3 Find Segment Lengths
Substitute 3 for XV.= 3
TUVW is a parallelogram.Find TX.
SOLUTION
TX = XV Diagonals of a bisect each other.
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