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6. Show that consecutive angles are supplementary

6. Show that consecutive angles are supplementary. What Makes a Quadrilateral a Parallelogram?. What do you see?. Are both pairs of opposite sides parallel?. In This Picture…. Is one pair of opposite sides congruent and parallel?. Are both pairs of opposite sides congruent?.

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6. Show that consecutive angles are supplementary

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  1. 6. Show that consecutive angles are supplementary

  2. What Makes a Quadrilateral a Parallelogram? What do you see? Are both pairs of opposite sides parallel?

  3. In This Picture… Is one pair of opposite sides congruent and parallel?

  4. Are both pairs of opposite sides congruent?

  5. Are both pairs of opposite angles congruent? What is this Picture?

  6. What is this?

  7. What is this?

  8. Is a Pentagon a Parallelogram? NO!

  9. 3. ANSWER Two pairs of opposite sides are equal. Therefore, the quadrilateral is a parallelogram. By theorem 8.7 for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  10. 4. ANSWER By theorem 8.8, if the opposite angles are Congruent, the quadrilateral is a parallelogram. for Examples 2 and 3 GUIDED PRACTICE What theorem can you use to show that the quadrilateral is a parallelogram?

  11. 5. For what value of xis quadrilateral MNPQa parallelogram? Explain your reasoning. 2x = 10 – 3x By Theorem 8.6 [ Diagonals in bisect each other ] 5x = 10 x = 2 for Examples 2 and 3 GUIDED PRACTICE SOLUTION Add 3xto each side Divide each side by 5

  12. 6. Show that consecutive angles are supplementary

  13. Game Time: Name that Theorem

  14. Game Time: Name that Theorem

  15. Game Time: Name that Theorem

  16. Game Time: Name that Theorem

  17. Game Time: Name that Theorem 6. Show that consecutive angles are supplementary

  18. Game Time: Name that Theorem

  19. Show that quadrilateral ABCDis a parallelogram. First use the Distance Formula to show that ABand CDare congruent. 29 [2 – (–3)]2 + (5 – 3)2 = 29 (5 – 0)2 + (2 – 0)2 = EXAMPLE 4 Use coordinate geometry SOLUTION One way is to show that a pair of sides are congruent and parallel. Then apply Theorem 8.9. AB = CD =

  20. 29 , AB BecauseAB = CD = CD. AB CD. Then use the slope formula to show that 5 – (3) 2 – 0 Slope of CD = = Slope of AB = = 5 – 0 2 – (–3) Because ABand CDhave the same slope, they are parallel. ANSWER ABand CDare congruent and parallel. So, ABCDis a parallelogram by Theorem 8.9. 2 2 5 5 EXAMPLE 4 Use coordinate geometry

  21. EXAMPLE 4 for Example 4 GUIDED PRACTICE 6.Refer to the Concept Summary. Explain how other methods can be used to show that quadrilateral ABCDin Example 4 is a parallelogram. SOLUTION Find the Slopes of all 4 sides and show that each opposite sides always have the same slope and, therefore, are parallel. Find the lengths of all 4 sides and show that the opposite sides are always the same length and, therefore, are congruent. Find the point of intersection of the diagonals and show the diagonals bisect each other.

  22. 65 65 [-4 – (0)]2 + (1 – 8)2 [4 – (8)]2 + (-1 – 6)2 = = EXAMPLE 4 for Example 4 GUIDED PRACTICE K DK and TAare congruent and parallel. So, TDKA is a parallelogram by Theorem 8.9. A D T DK = TA =

  23. In Conclusion…

  24. Don’t forget your homework. • Pg 526 # 1-3, 11-14

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