Warm Up Find the value of each variable. 1. x2. y3. z 218 4

Sections 8-2 & 8-3 Parallelograms

A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol. What is a Parallelogram?

Properties of Parallelograms? Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. If a has one right angle, then it has 4 right angles.

What about the diagonals? The diagonals of a parallelogram bisect each other. Each diagonal of a parallelogram separates the parallelogram into 2 congruent triangles.

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. CF = 74 mm Applying Properties of Parallelograms: Find mEFCmEFC = 138° Find DFDF = 62

Example: Using Properties of Parallelograms to Find Measures WXYZ is a parallelogram. Find YZ. YZ = 52 Find mZ. m  Z = 65

Example: EFGH is a parallelogram. Find JG. JG = 12 Find FH. FH =18

Lesson Quiz: Part I In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure. 1. PW 2. mPNW 18144°

Lesson Quiz: Part II QRST is a parallelogram. Find each measure. 2. TQ 3. mT 28 71°

Area of a Parallelogram? Find the area of the parallelogram. A = 176 mm 2

Example: Find the base of the parallelogram in which h = 56 yd and A = 28 yd 2. b = 0.5 yd

To prove a quadrilateral is a parallelogram, use any one of these conditions:

Example: Applying Conditions for Parallelograms Determine if the quadrilateral must be a parallelogram. Justify your answer. No. Only one pair of opposite angles are congruent.

Example: Determine if the quadrilateral must be a parallelogram. Justify your answer. The diagonal of the quadrilateral forms 2 congruent triangles. Yes

Example: Determine if each quadrilateral must be a parallelogram. Justify your answer. No. None of the sets of conditions for a parallelogram are met.

To Prove Parallelograms on the Coordinate Plane: Given vertices as ordered pairs. Compare Slopes Slopes and Distance Formula Use Midpoint Formula

No; One pair of consecutive s are , and one pair of opposite sides are ||. The conditions for a parallelogram are not met. Lesson Quiz 1. Show that JKLM is a parallelogram for a = 4 and b = Determine if QWRT must be a parallelogram. Justify your answer. JN = LN = 22; KN = MN = 10; so JKLM is a parallelogram by Theorem