Geometry Lesson 6 2 Parallelograms Objective Recognize and

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.

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

Theorems: Properties of Parallelograms Theorem 6. 3 l If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Theorem 6. 4 l If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Theorem 6. 5 l If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

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

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

Theorems: Diagonals of Parallelograms Theorem 6. 7 l If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Theorem 6. 8 l If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

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

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

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? l Since we know they bisect what is a good point to find? l Find the Midpoint of the diagonals: l Double check:

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)

Statements Reasons 1. Given 2. Opp. Sides congruent. 3. Transitive

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