Find the value of each variable. 1. x 2. y 3. z

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Angle Relationships in TrianglesProperties of ParallelogramsFind the value of each variable.

1. x 2. y 3. z

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Angle Relationships in TrianglesProperties of Parallelograms

A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol .

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Example 1A: Properties of Parallelograms

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°.

Find CF.

Find mEFC.

Find DF.

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Example 2A: Using Properties of Parallelograms to Find Measures

WXYZ is a parallelogram.

Find YZ.

Find mZ

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Example 2a

EFGH is a parallelogram.

Find JG.

Find FH.

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A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.

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Since a rectangle is a parallelogram by, a rectangle “inherits” all the properties of parallelograms.

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Example 1: Craft Application

A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

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A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.

Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

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Example 2A: Using Properties of Rhombuses to Find Measures

TVWX is a rhombus.

Find TV.

Find mVTZ.

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A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

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Lesson Review: Part I

In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure.

1. PW 2. mPNW

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Lesson Review: Part II

QRST is a parallelogram. Find each measure.

2. TQ 3. mT

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Lesson Review: Part III

PQRS is a rhombus. Find each measure.

3. QP 4. mQRP

Find the value of each variable. 1. x 2. y 3. z

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