1. Geometry Lesson 6 – 2 Parallelograms Objective: Recognize and apply properties of the sides of angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms.

2. Parallelograms What is a parallelogram? A quadrilateral with both pairs of opposite sides parallel. To name a parallelogram:

3. Theorems: Properties of Parallelograms Theorem 6.3 If a quadrilateral is a parallelogram, then its opposite sides are congruent.

4. Theorem Theorem 6.4 If a quadrilateral is a parallelogram, then its opposite angles are congruent.

5. Theorem Theorem 6.5 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

6. Theorem Theorem 6.6 If a parallelogram has one right angle, then it has four right angles.

7. In parallelogram ABCD, suppose the measure of angle A is 55, segment AB is 2.5 feet, and segment BC is 1 foot. Find each measure. Find DC 2.5 180 – 55 = 125 55

8. Theorems: Diagonals of Parallelograms Theorem 6.7 If a quadrilateral is a parallelogram, then its diagonals bisect each other.

9. Theorem Theorem 6.8 If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

10. If QRST is a parallelogram, find the following. Find x Find y Find z 5x = 27 x = 5.4 2y – 5 = y + 4 y = 9 3z = 33 z = 11 Opps. Sides equal Diagonals bisect Alt. Interior angles are congruent.

11. Find the value of each variable in the parallelograms. 4x + 2x – 6 = 180 6x – 6 = 180 6x = 186 x = 31 y + 8 = 5y 2 = y 3z – 4 = z + 5 2z = 9 z = 4.5

12. Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices F (-2, 4) G (3, 5) H (2, -3) and J (-3, -4) What do you know about the diagonals of a parallelogram? Since we know they bisect what is a good point to find? Find the Midpoint of the diagonals: Double check:

13. Determine the coordinates of the intersection of the diagonals of RSTU with vertices R (-8, -2) S (-6, 7) T (6, 7) and U (4, -2)

14. StatementsReasons 1. 1. Given 2. 2. Opp. Sides congruent. 3.3. Transitive

15. Homework Pg. 403 1 – 6 all, 10 – 22 E, 44 – 60 E