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. 7/3/ : Parallelograms

Quadrilaterals Defn: Quadrilateral: A polygon is a quadrilateral iff it has exactly 4 sides. 7/3/ : Parallelograms

Parallelograms Defn: Parallelogram: A quadrilateral is a parallelogram iff both pair of opposite sides are parallel. 7/3/ : Parallelograms

Parallelograms 7/3/ : Parallelograms

Parallelograms A D C B Parallelogram ABCD 7/3/ : Parallelograms

Diagonals Defn: Diagonal of a Polygon: A diagonal of a polygon is a segment whose endpoints are any 2 nonconsecutive vertices of the polygon. 7/3/ : Parallelograms

Diagonals A D C B AC and BD are diagonals. 7/3/ : Parallelograms

Properties of a Parallelogram Theorem: If a quadrilateral is a parallelogram: a. Both pairs of opposite sides are congruent. b. Both pairs of opposite angles are congruent. c. Consecutive angles are supplementary. d. The diagonals bisect each other. 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. A B D C 105° a. What are the parallel sides? 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. B A D C 105° b. Name the congruent angles. 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. c. Name the congruent sides. A D C 105° B 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. d. Determine the measures of each of the remaining angles. A D C 105° B 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. e. Give a pair of supplementary angles. A D C 105° B 7/3/ : Parallelograms

Use parallelogram ABCD below to answer the following questions. A B D C f. If AC and BD intersect at M and AM = 12, what is AC? M 7/3/ : Parallelograms

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

In the parallelogram below, PS is 7 centimeters long. If the parallelogram’s perimeter is 40 centimeters, how many centimeters long is PQ? A. 49 B. 21 C. 13 D. 10 E. 5.7 P S R Q 7/3/ : Parallelograms

Prove both pairs of opposite angles of a parallelogram are congruent. 7/3/ : Parallelograms

Given: parallelogram ABCD Prove: ∠ A ≅ ∠ C and ∠ B ≅∠ D A B C D 7/3/ : Parallelograms

Assignment pages , #17 – 29 (odds), 37 7/3/ : Parallelograms