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

Find the value of each variable. 1. x 2. y 3. z. A quadrilateral with two pairs of parallel sides is a parallelogram . To write the name of a parallelogram, you use the symbol. In CDEF , DE = 74 mm, DG = 31 mm, and m  FCD = 42° . Find CF. Find m  EFC. Find DF.

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

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  1. Find the value of each variable. 1.x2.y 3.z

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

  3. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Find mEFC. Find DF. Example 1A: Properties of Parallelograms

  4. Example 2A: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find YZ. Find mZ

  5. Example 2a EFGH is a parallelogram. Find JG. Find FH.

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

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

  8. Example 1: Craft Application A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

  9. A rhombus is another special quadrilateral. A rhombusis a quadrilateral with four congruent sides. Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

  10. Example 2A: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find TV. Find mVTZ.

  11. 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.

  12. Lesson Review: Part I In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure. 1.PW2. mPNW

  13. Lesson Review: Part II QRST is a parallelogram. Find each measure. 2.TQ3. mT

  14. Lesson Review: Part III PQRS is a rhombus. Find each measure. 3.QP4. mQRP

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