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8.2/8.3 Parallelograms

8.2/8.3 Parallelograms. Vocabulary. Parallelograms. What You'll Learn. You will learn to identify and use the properties of parallelograms. 1) Parallelogram. In parallelogram ABCD below, and . B. A. D. C. Parallelograms. parallel sides.

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8.2/8.3 Parallelograms

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  1. 8.2/8.3 Parallelograms

  2. Vocabulary Parallelograms What You'll Learn You will learn to identify and use the properties of parallelograms. 1) Parallelogram

  3. In parallelogram ABCD below, and B A D C Parallelograms parallel sides A parallelogram is a quadrilateral with two pairs of ____________. congruent Also, the parallel sides are _________. Knowledge gained about “parallels” (chapter 4)will now be used in the following theorems.

  4. A A A B B B D D D C C C Parallelograms Opposite angles of a parallelogram are ________. congruent A  C and B  D Opposite sides of a parallelogram are ________. congruent The consecutive angles of a parallelogram are ____________. supplementary mA + mB = 180mD + mC = 180

  5. In RSTU, RS = 45, ST = 70, and U = 68. S R 45 70 U T 68° Parallelograms Find: RU = ____ 70 Theorem 8-3 45 UT = _____ Theorem 8-3 68° Theorem 8-2 mS = _____ 112° Theorem 8-4 mT = _____

  6. In RSTU, if RT = 56, find RE. A B R D S C E U T Parallelograms bisect E RE = 28

  7. A B D C Parallelograms In the figure below, ABCD is a parallelogram. Since AD || BC and diagonal DB is a transversal, then ADB  CBD. (Alternate Interior angles) Since AB || DC and diagonal DB is a transversal, then BDC  DBA. (Alternate Interior angles) DB  BD ASA Theorem

  8. A B D C Parallelograms congruent triangles

  9. Parallelograms The Escher design below is based ona _____________. parallelogram You can use a parallelogram to make a simple Escher-like drawing. Change one side of the parallelogram and then translate (slide) the change to the opposite side. The resulting figure is used to make a design with different colors and textures.

  10. Parallelograms End of Section 8.2

  11. Vocabulary Tests for Parallelograms What You'll Learn You will learn to identify and use tests to show that a quadrilateral is a parallelogram. Nothing New!

  12. A B C D Tests for Parallelograms congruent

  13. In quadrilateral PQRS, PR and QS bisect each other at T. P Q T S R Tests for Parallelograms You can use the properties of congruent triangles and Theorem 8-7 to find other ways to show that a quadrilateral is a parallelogram. Show that PQRS is a parallelogram by providing a reason for each step. Definition of segment bisector Vertical angles are congruent SAS Corresp. parts of Congruent Triangles are Congruent Theorem 8-7

  14. A B C D Tests for Parallelograms parallel congruent

  15. A B E D C Tests for Parallelograms bisect each other

  16. A B D C Tests for Parallelograms Determine whether each quadrilateral is a parallelogram.If the figure is a parallelogram, give a reason for your answer. Given Alt. Int. Angles Therefore, quadrilateral ABCD is a parallelogram. Theorem 8-8

  17. Tests for Parallelograms End of Section 8.3

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