Properties of Parallelograms 6-2 Properties of Parallelograms Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

Warm up: 90+90+67+x=360 247+x=360 x=113 2x+13+153+3x-1+8x=360 13x+165=360 13x=195 x=15

Objectives Use properties of parallelograms to solve problems.

Any polygon with four sides is a _______________. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names. For example…. A parallelogram is To write the name of a parallelogram, you use the symbol quadrilateral a quadrilateral with both pairs of opposite sides being parallel.

Properties of parallelograms Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other.

a. FGHJ is a parallelogram. Find JH and FJ. 5 3

b. ABCD is a parallelogram. Find AB and AD. 8 9

c. PQRS is a parallelogram. Find the missing angle measures. 70 110 110

d. ABCD is a parallelogram. Find the missing angle measures. 120 120 60

e. TUVW is a parallelogram. Find TX. 3

4. 5. 6. y=98 2x=4 x=12 x=2 180-98=x 3y+1=10 y-1=6 x=82 3y=9 y=7 y=3

Example 7 EFGH is a parallelogram. Find JG.  diags. bisect each other. 3w = w + 8 Substitute. 2w = 8 Simplify. w = 4 Divide both sides by 2. JG = w + 8 = 4 + 8 = 12

Exmaple 8 EFGH is a parallelogram. Find FH.  diags. bisect each other. 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

Example 9 WXYZ is a parallelogram. Find YZ.  opp. sides  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

Example 10 WXYZ is a parallelogram. Find mZ . mZ + mW = 180°  cons. s supp. (9b + 2) + (18b – 11) = 180 Substitute the given values. 27b – 9 = 180 Combine like terms. 27b = 189 Add 9 to both sides. b = 7 Divide by 27. mZ = (9b + 2)° = [9(7) + 2]° = 65°

QRST is a parallelogram. Find each measure. 11. TQ

12. mS

12. MR