Find the value of each variable. 1. x 2. y 3. z
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04/21/23
Angle Relationships in TrianglesProperties of ParallelogramsFind the value of each variable.
1. x 2. y 3. z
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04/21/23
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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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Example 2A: Using Properties of Parallelograms to Find Measures
WXYZ is a parallelogram.
Find YZ.
Find mZ
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Example 2a
EFGH is a parallelogram.
Find JG.
Find FH.
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Since a rectangle is a parallelogram by, a rectangle “inherits” all the properties of parallelograms.
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Example 2A: Using Properties of Rhombuses to Find Measures
TVWX is a rhombus.
Find TV.
Find mVTZ.
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
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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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Lesson Review: Part I
In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure.
1. PW 2. mPNW
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Lesson Review: Part II
QRST is a parallelogram. Find each measure.
2. TQ 3. mT
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04/21/23
Angle Relationships in TrianglesProperties of Parallelograms
Lesson Review: Part III
PQRS is a rhombus. Find each measure.
3. QP 4. mQRP