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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. 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. Properties of Parallelograms?.

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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. 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. Lesson Quiz: Part I 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.

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

  19. Lesson Quiz: Part II 3. Show that the quadrilateral with vertices E(–1, 5), F(2, 4), G(0, –3), and H(–3, –2) is a parallelogram. Since one pair of opposite sides are || and , EFGH is a parallelogram by Theorem 6-3-1.

  20. Example: Proving Parallelograms in the Coordinate Plane Show that quadrilateral JKLM is a parallelogram by using the definition of parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0). Find the slopes of both pairs of opposite sides. Since both pairs of opposite sides are parallel, JKLM is a parallelogram by definition.

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