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Monday, August 26th

Monday, August 26th. Warm Up. 2. Solve for Z. Solve for x and Y. Homework Answers. Any polygon with four sides is a quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names. Helpful Hint.

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Monday, August 26th

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  1. Monday, August 26th Warm Up 2. Solve for Z Solve for x and Y

  2. Homework Answers

  3. Any polygon with four sides is a quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names.

  4. Helpful Hint Opposite sides of a quadrilateral do not share a vertex. Opposite angles do not share a side. Parallelograms

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

  6. I. The Properties of Parallelograms A B • Opposite sides are congruent (AB=DC) • Opposite angles are congruent (D=B) • Consecutive angles are supplementary (A+D=180) • If one angle is right, then all angles are right. • The diagonals of a parallelogram bisect each other. • Each diagonal of a parallelogram separates it into two congruent triangles. C D

  7. II. Finding Missing Angles and Lengths

  8. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. opp. sides Example 1 Part A CF = DE Def. of segs. CF = 74 mm Substitute 74 for DE.

  9. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC. cons. s supp. Example 1 Part B mEFC + mFCD = 180° mEFC + 42= 180 Substitute 42 for mFCD. mEFC= 138° Subtract 42 from both sides.

  10. #2 You Try! In PNWL, NW = 12, PM = 9, and mWLP= 144°. Find each measure. 1.PW2.mPNW 144° 18

  11. III. Using Algebra

  12. opp. s  Example 1A WXYZ is a parallelogram. Find YZ. YZ = XW Def. of  segs. 8a – 4 = 6a + 10 Substitute the given values. Subtract 6a from both sides and add 4 to both sides. 2a = 14 a = 7 Divide both sides by 2. YZ = 8a – 4 = 8(7) – 4 = 52

  13. cons. s supp. Example 1B WXYZ is a parallelogram. Find mZ. mZ + mW = 180° (9b + 2)+ (18b –11) = 180 Substitute the given values. Combine like terms. 27b – 9 = 180 27b = 189 b = 7 Divide by 27. Answer: mZ= (9b + 2)° = [9(7) + 2]° = 65°

  14. diags. bisect each other. You Try! #2 A EFGH is a parallelogram. Find JG. Def. of  segs. EJ = JG Substitute. 3w = w + 8 Simplify. 2w = 8 Divide both sides by 2. w = 4 JG = w + 8 = 4 + 8 = 12

  15. diags. bisect each other. #2 Part B EFGH is a parallelogram. Find FH. FJ = JH Def. of  segs. 4z – 9 = 2z Substitute. 2z = 9 Simplify. z = 4.5 Divide both sides by 2. FH = (4z – 9) + (2z) = 4(4.5) – 9 + 2(4.5) = 18

  16. #3 You Try! QRST is a parallelogram. Find each measure. 2.TQ3.mT 28 71°

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