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6-1: Parallelograms

6-1: Parallelograms. Expectation: G1.4.1: Solve multi-step problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelogram, kites and trapezoids. Quadrilaterals.

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6-1: Parallelograms

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  1. 6-1: Parallelograms • Expectation: • G1.4.1: Solve multi-step problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelogram, kites and trapezoids. 6-1: Parallelograms

  2. Quadrilaterals Defn: Quadrilateral: A polygon is a quadrilateral iff it has exactly 4 sides. 6-1: Parallelograms

  3. Parallelograms Defn: Parallelogram: A quadrilateral is a parallelogram iff both pair of opposite sides are parallel. 6-1: Parallelograms

  4. Parallelograms 6-1: Parallelograms

  5. Parallelograms D C B A Parallelogram ABCD 6-1: Parallelograms

  6. Diagonals Defn: Diagonal of a Polygon: A diagonal of a polygon is a segment whose endpoints are any 2 nonconsecutive vertices of the polygon. 6-1: Parallelograms

  7. AC and BD are diagonals. Diagonals D C A B 6-1: Parallelograms

  8. Properties of a Parallelogram Theorem: • If a quadrilateral is a parallelogram: • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • Consecutive angles are supplementary. • The diagonals bisect each other. 6-1: Parallelograms

  9. D C 105° A B Use parallelogram ABCD below to answer the following questions. a. What are the parallel sides? 6-1: Parallelograms

  10. D C 105° A Use parallelogram ABCD below to answer the following questions. B b. Name the congruent angles. 6-1: Parallelograms

  11. D C 105° A Use parallelogram ABCD below to answer the following questions. B c. Name the congruent sides. 6-1: Parallelograms

  12. D C 105° A Use parallelogram ABCD below to answer the following questions. B d. Determine the measures of each of the remaining angles. 6-1: Parallelograms

  13. D C 105° A Use parallelogram ABCD below to answer the following questions. B e. Give a pair of supplementary angles. 6-1: Parallelograms

  14. Use parallelogram ABCD below to answer the following questions. D C M A B f. If AC and BD intersect at M and AM = 12, what is AC? 6-1: Parallelograms

  15. Three vertices of a parallelogram are (2,3), (5,7) and (3,8). What are all possible coordinates for the fourth vertex? 6-1: Parallelograms

  16. In the parallelogram below, PS is 7 centimeters long. If the parallelogram’s perimeter is 40 centimeters, how many centimeters long is PQ? • 49 • 21 • 13 • 10 • 5.7 P Q S R 6-1: Parallelograms

  17. Prove both pairs of opposite angles of a parallelogram are congruent. 6-1: Parallelograms

  18. Given: parallelogram ABCD Prove: ∠A ≅∠C and ∠B ≅∠D D C B A 6-1: Parallelograms

  19. Assignment pages 295-296, #17 – 29 (odds), 37 6-1: Parallelograms

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