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Understanding Properties of Parallelograms: Angle and Side Calculations

Explore the essential properties of parallelograms, including rhombuses and rectangles, through practical examples. This guide focuses on calculating angle measures and side lengths using the properties of these quadrilaterals. Learn to recognize that a quadrilateral with two pairs of parallel sides is a parallelogram, and apply the formulas to solve problems effectively. By engaging with practical exercises, discover how opposite sides are equal and angles are supplementary, reinforcing your understanding of geometry.

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Understanding Properties of Parallelograms: Angle and Side Calculations

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  1. Math 1 Warm-ups 1-15-09 Copy and Find the value of each angle

  2. Parallelogram Rhombus Kite Parallelogram Rectangle Parallelogram Rectangle Rhombus Square Parallelogram Trapezoid

  3. Objectives Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

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

  5. Properties of Parallelograms

  6. Properties of Parallelograms………….continued

  7. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. opp. sides Properties of Parallelograms CF = DE Def. of segs. CF = 74 mm Substitute 74 for DE.

  8. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC. cons. s supp. Properties of Parallelograms mEFC + mFCD = 180° mEFC + 42= 180 Substitute 42 for mFCD. mEFC = 138° Subtract 42 from both sides.

  9. diags. bisect each other. Example In KLMN, LM = 28 in., LN = 26 in., and mLKN = 74°. Find LO. LN = 2LO 26 = 2LO Substitute 26 for LN. LO = 13 in. Simplify.

  10. opp. s  Using Properties of Parallelograms to Find Measures 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

  11. cons. s supp. Using Properties of Parallelograms to Find Measures 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. mZ = (9b + 2)° = [9(7) + 2]° = 65°

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