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

Warm Up Find the value of each variable. 1. x 2. y 3. z. 2. 18. 4. Sections 8-2 & 8-3. Parallelograms. What is a Parallelogram?. 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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Warm Up Find the value of each variable. 1. x 2. y 3. z

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  1. Warm Up Find the value of each variable. 1.x2.y 3.z 2 18 4

  2. Sections 8-2 & 8-3 Parallelograms

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

  4. Properties of Parallelograms? • Opposite sides are congruent. • Opposite angles are congruent. • Consecutive angles are supplementary. • If a has one right angle, then it has 4 right angles.

  5. What about the diagonals? • The diagonals of a parallelogram bisect each other. • Each diagonal of a parallelogram separates the parallelogram into 2 congruent triangles.

  6. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Applying Properties of Parallelograms: CF = 74 mm Find mEFC mEFC = 138° Find DF DF = 62

  7. Example: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find YZ. YZ = 52 Find mZ. mZ = 65

  8. Example: EFGH is a parallelogram. Find JG. JG = 12 Find FH. FH =18

  9. Lesson Quiz: Part I In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure. 1.PW2. mPNW 18 144°

  10. Lesson Quiz: Part II QRST is a parallelogram. Find each measure. 2.TQ3. mT 71° 28

  11. Area of a Parallelogram? Find the area of the parallelogram. A = 176 mm2

  12. Example: Find the base of the parallelogram in which h = 56 yd and A = 28 yd2. b = 0.5 yd

  13. To prove a quadrilateral is a parallelogram, use any one of these conditions:

  14. Example: Applying Conditions for Parallelograms Determine if the quadrilateral must be a parallelogram. Justify your answer. No. Only one pair of opposite angles are congruent.

  15. Example: Determine if the quadrilateral must be a parallelogram. Justify your answer. Yes The diagonal of the quadrilateral forms 2 congruent triangles.

  16. Example: Determine if each quadrilateral must be a parallelogram. Justify your answer. No. None of the sets of conditions for a parallelogram are met.

  17. To Prove Parallelograms on the Coordinate Plane: • Given vertices as ordered pairs. Compare Slopes Slopes and Distance Formula Use Midpoint Formula

  18. Lesson Quiz 1. Show that JKLM is a parallelogram for a = 4 and b = 5. 2. Determine if QWRT must be a parallelogram. Justify your answer. JN = LN = 22; KN = MN = 10; so JKLM is a parallelogram by Theorem 6-3-5. No; One pair of consecutive s are , and one pair of opposite sides are ||. The conditions for a parallelogram are not met.

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