Section 6.2: Parallelograms

Section 6.2: Parallelograms EQ: What are the properties of parallelograms?

Vocab! A quadrilateral with both pairs of opposite sides parallel If JKLM is a parallelogram then J K L M If JKLM is a parallelogram, then ∠J ≅ ∠L and ∠M ≅ ∠K J K L M

Example 1 In parallelogram ABCD, suppose m∠B= 32, CD = 80 inches, and BC = 15 inches. Find AD AD = BC AD = 15 b) Find m∠C 32 + 32 = 64 360 – 64 = 296 296/2 = 148 148° c) Find m∠D m∠D = m∠B m∠D = 32°

Example 2 Find the values of x and y.

You Try! m∠E = m∠G m∠G = 60° 2x = 50 x = 25 ML = JK y + 3 = 18 y = 15

Consecutive interior angles theorem… x + y = 180°

Vocab! J K y x y x L M A B P D C

Example 2 • Find AB • m∠C • m∠D AB = DC AB = 30 m∠C = m∠A m∠C = 36° 180 – 36 = 144°

Example 3 If WXYZ is a parallelogram… • Find the value of r. b) Find the value of s. c) Find the value of t. WX = ZY 4r = 18 r = 4.5 7s + 3 = 8s s = 3 Alternate Interior Angles 2t = 18 t = 9

You Try! Find the indicated measure in parallelogram LMNQ. Explain your reasoning. 1.LM 2. LP 3. LQ 4. MQ LM = QN 13 LP = NP 7 LQ = MN 8 MP = QP QP = 8.2 QP + MP = MQ 16.4

You Try Cont. 5. 6. 7. 8. 180 – 100 = ∠LMN m∠LMN = 80° m∠NQL = m∠LMN 80° m∠MNQ = m∠MLQ 100° Alternate interior angles m∠LMQ= m∠NQM 29°

Coordinate Geometry

Example 4 a) What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4) and R(3, 1)? Need to find the midpoint of Midpoint formula: , = (1, 2) = (1, 2) Diagonal intersection= (1, 2) P N R M

Example 4 cont. b) What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0, –3), M(–2, 1), N(1, 5) and O(3, 1)? Need to find the midpoint of Midpoint formula: , = () = () Diagonal intersection: N M O L

Section 6.2: Parallelograms