Section 6 2 Parallelograms EQ What are the

Vocab! Parallelogram Opposite Sides Theorem Parallelogram Opposite Angles Theorem A quadrilateral with both pairs

Example 1 In parallelogram ABCD, suppose m∠B = 32 , CD = 80 inches,

You Try! 1. Find FG and the measure of angle G. m∠E = m∠G

Consecutive interior angles theorem… x + y = 180°

Vocab! Parallelogram Consecutive If JKLM is a parallelogram, then x + y = 180°

Example 2 a) Find AB AB = DC AB = 30 b) m∠C =

Example 3 If WXYZ is a parallelogram… a) Find the value of r. WX

You Try! Find the indicated measure in parallelogram LMNQ. Explain your reasoning. 1. LM

You Try Cont. • 180 – 100 = ∠LMN m∠LMN = 80° m∠NQL =

Coordinate Geometry Using a coordinate grid to prove certain relationships about polygons. Using coordinate

Example 4 a) What are the coordinates of the intersection of the diagonals of

Example 4 cont. b) What are the coordinates of the intersection of the diagonals

Slides: 14

Download presentation

Section 6. 2: Parallelograms EQ: What are the properties of parallelograms?

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

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

Example 2 Find the values of x and y.

You Try! 1. Find FG and the measure of angle G. m∠E = m∠G = 60° 2. Find the values of x and y.

Consecutive interior angles theorem… x + y = 180°

Vocab! Parallelogram Consecutive If JKLM is a parallelogram, then x + y = 180° Angles Theorem J K y x M Parallelogram Diagonals Theorem y x L If ABCD is a parallelogram then AP = PC and DP = PB A B P D C

Example 2 a) Find AB AB = DC AB = 30 b) m∠C = m∠A m∠C = 36° c) m∠D 180 – 36 = 144°

Example 3 If WXYZ is a parallelogram… a) Find the value of r. WX = ZY 4 r = 18 r = 4. 5 b) Find the value of s. 7 s + 3 = 8 s s = 3 c) Find the value of t. Alternate Interior Angles 2 t = 18 t = 9

You Try! Find the indicated measure in parallelogram LMNQ. Explain your reasoning. 1. LM LM = QN 13 2. LP = NP 7 3. LQ LQ = MN 8 4. MQ MP = QP QP = 8. 2 QP + MP = MQ 16. 4

You Try Cont. • 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 Using a coordinate grid to prove certain relationships about polygons. Using coordinate geometry, how can you prove a shape is a parallelogram? Use theorems to prove the shape is a parallelogram.

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)? 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)? N M O L