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Identify and Solve Problems with Parallelograms

Learn how to identify and understand the properties of parallelograms, find side lengths and angle measures, and calculate segment lengths in this daily warm-up exercise. Complete the quiz and practice problems to reinforce your knowledge of parallelograms.

williambradshaw
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Identify and Solve Problems with Parallelograms

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  1. Warm Up 6.2on desk Do Daily Quiz 6.1

  2. Section 6.2 Use properties of parallelograms. EQ: How do you identify a parallelogram?

  3. Parallelogram • a quadrilateral with both pairs of opposite sides parallel.

  4. Theorem 6.2 • If a quadrilateral is a parallelogram, then its opposite sides are congruent.

  5. Theorem

  6. Example 1 Find Side Lengths of Parallelograms FGHJ is a parallelogram. Find JH and FJ. SOLUTION JH=FG =5 FJ=GH =3 ANSWER In FGHJ, JH =5 and FJ = 3.

  7. Checkpoint Find Side Lengths of Parallelograms ABCD is a parallelogram. Find AB and AD. AB = 9; AD = 8 ANSWER

  8. Theorem 6.3 • If a quadrilateral is a parallelogram, then its opposite angles are congruent.

  9. Theorem

  10. Theorem 6.4 • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

  11. Theorem

  12. Theorem

  13. Example 2 Find Angle Measures of Parallelograms PQRS is a parallelogram. Find the missing angle measures. SOLUTION By Theorem 6.3, so mP= mR=70°. By Theorem 6.4, mQ + mP =180° mQ + 70°=180° mQ=110° so mQ= mS=110

  14. Checkpoint Find Angle Measures of Parallelograms ABCD is a parallelogram. Find the missing angle measures. mB=120°; mC=60° mD =120° ANSWER mA=75°; mB=105° mC =75° ANSWER

  15. Follow Up

  16. Theorem 6.5 • If a quadrilateral is a parallelogram, then its diagonals bisect each other.

  17. Theorem

  18. Theorem

  19. Example 3 Find Segment Lengths TUVW is a parallelogram. Find TX. SOLUTION TX= XV =3

  20. Homework

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