Bell Ringer

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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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3.

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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