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A quadrilateral with two pairs of parallel sides is a parallelogram . To write the name of a parallelogram, you use the symbol . Go to the following videos to see how to work the next problems. http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6551/6551.xml

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

  2. Go to the following videos to see how to work the next problems. http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6551/6551.xml http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6754/6754.xml http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6755/6755.xml

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

  4. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find mEFC. cons. s supp. Example 1B: 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.

  5. In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find DF. diags. bisect each other. Example 1C: Properties of Parallelograms DF = 2DG DF = 2(31) Substitute 31 for DG. DF = 62 Simplify.

  6. Watch this video. It will help with your homework worksheet. http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6754/6754.xml

  7. diags. bisect each other. Check It Out! Example 2a EFGH is a parallelogram. Find JG. EJ = JG Def. of  segs. 3w = w + 8 Substitute. 2w = 8 Simplify. w = 4 Divide both sides by 2. JG = w + 8 = 4 + 8 = 12

  8. diags. bisect each other. Check It Out! Example 2b 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

  9. The two theorems below can also be used to show that a given quadrilateral is a parallelogram.

  10. http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6552/6552.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6552/6552.xml

  11. Example 1A: Verifying Figures are Parallelograms Show that JKLM is a parallelogram for a = 3 and b = 9. Step 1 Find JK and LM. Given LM = 10a + 4 JK = 15a – 11 Substitute and simplify. LM = 10(3)+ 4 = 34 JK = 15(3) – 11 = 34

  12. Example 1A Continued Step 2 Find KL and JM. Given KL = 5b + 6 JM = 8b – 21 Substitute and simplify. KL = 5(9) + 6 = 51 JM = 8(9) – 21 = 51 Since JK = LM and KL = JM, JKLM is a parallelogram by Theorem 6-3-2.

  13. Example 1B: Verifying Figures are Parallelograms Show that PQRS is a parallelogram for x = 10 and y = 6.5. mQ = (6y + 7)° Given Substitute 6.5 for y and simplify. mQ = [(6(6.5) + 7)]° = 46° mS = (8y – 6)° Given Substitute 6.5 for y and simplify. mS = [(8(6.5) – 6)]° = 46° mR = (15x – 16)° Given Substitute 10 for x and simplify. mR = [(15(10) – 16)]° = 134°

  14. Example 1B Continued Since 46° + 134° = 180°, R is supplementary to both Q and S. PQRS is a parallelogram by Theorem 6-3-4.

  15. http://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6757/6757.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/geo/player.html?contentSrc=6757/6757.xml

  16. Example 2A: Applying Conditions for Parallelograms Determine if the quadrilateral must be a parallelogram. Justify your answer. Yes. The 73° angle is supplementary to both its corresponding angles. By Theorem 6-3-4, the quadrilateral is a parallelogram.

  17. You have learned several ways to determine whether a quadrilateral is a parallelogram. You can use the given information about a figure to decide which condition is best to apply.

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