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5.1 Properties of Parallelograms

5.1 Properties of Parallelograms. Geometry Ms. Kelly Fall 2010. Objectives:. Apply the definition of a parallelogram and the theorems about properties of a parallelogram. In this lesson.

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5.1 Properties of Parallelograms

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  1. 5.1 Properties of Parallelograms Geometry Ms. Kelly Fall 2010

  2. Objectives: • Apply the definition of a parallelogram and the theorems about properties of a parallelogram.

  3. In this lesson . . . And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram to the right, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

  4. Opposite sides of a parallelograms are parallel!!! Duh!

  5. 5.1 Opposite sides of a parallelogram are __________. ►PQ≅RS and SP≅QR Theorems about parallelograms Q R P S

  6. 5.2 Opposite angles of a parallelogram are ____________. P ≅ R and Q ≅ S Theorems about parallelograms Q R P S

  7. 5.3 Diagonals of a parallelogram ____ each other. QM ≅ SM and PM ≅ RM Theorems about parallelograms Q R P S

  8. FGHJ is a parallelogram. Find the unknown length. JH JK Answers: JH =5 JK = 3 Ex. 1: Using properties of Parallelograms 5 G F 3 K H J b.

  9. Consecutive angles of a parallelogram are supplementary!

  10. PQRS is a parallelogram. Find the angle measure. mR mQ a. mR = mP mR = 70° mQ + mP = 180° mQ + 70° = 180° mQ = 110° Ex. 2: Using properties of parallelograms Q R 70° P S

  11. Try it… If quadrilateral RSTU is a parallelogram find the values of x, y, a, and b.

  12. Check for Understanding Page 168 3-7 For numbers 5-7, only answer yes or no if it can be a parallelogram 3. 4. 5. 6. 7.

  13. One final example… • Find the values of x and y… • Systems of equations!! 27 18 2x + 8y 4x – 2y

  14. Graded assignments Worksheet Practice B collected and graded Homework page 169-170 1-13, 19-24

  15. Closure (on little piece of paper) Name 5 properties of parallelograms. • opp. Sides are // • Opp. Sides are cong • Opp. Angles are cong • Diagonals bisect each other • Consec angles are supp

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