Then: You classified polygons with four sides as quadrilaterals. Now: 1.Recognize and apply properties of the sides and angles of parallelograms. 2.Recognize.

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Presentation transcript:

Then: You classified polygons with four sides as quadrilaterals. Now: 1.Recognize and apply properties of the sides and angles of parallelograms. 2.Recognize and apply the properties of diagonals of parallelograms. 6.2 PARALLELOGRAMS

PARALLELOGRAM

PROPERTIES OF PARALLELOGRAMS

Theorem 6.4 If a quadrilateral is a parallelogram, then its opposite angles are congruent. If ABCD is a parallelogram then  A   C and  B   D. PROPERTIES OF PARALLELOGRAMS

Theorem 6.5 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. If ABCD is a parallelogram then m  A + m  D = 180 and m  B + m  C = 180. PROPERTIES OF PARALLELOGRAMS

Theorem 6.6 If a parallelogram has one right angle, then it has four right angles. In ABCD, if  A is a right angle, then  B,  C, and  D are also right angles. PROPERTIES OF PARALLELOGRAMS

Use ABCD to find each measure. a.AB b.m  C c.m  B d.AD EXAMPLE 1A:

CONSTRUCTION In parallelogram ABCD, suppose m  B = 32, CD = 80 inches, BC = 15 inches. a.Find AD. b.Find m  C EXAMPLE 1B

DIAGONALS OF PARALLELOGRAMS

Theorem 6.8 If a quadrilateral is parallelogram, then each diagonal separates the parallelogram into two congruent triangles. If ABCD is a parallelogram, then  ABD   CDB. DIAGONALS OF PARALLELOGRAMS

EXAMPLE 2 A: USE PROPERTIES OF PARALLELOGRAMS AND ALGEBRA

EXAMPLE 2 B: USE PROPERTIES OF PARALLELOGRAMS AND ALGEBRA

EXAMPLE 2 C: USE PROPERTIES OF PARALLELOGRAMS AND ALGEBRA

If WXYZ is a parallelogram, find the value of the indicated variable. r = s = t = EXAMPLE 2 D: USE PROPERTIES OF PARALLELOGRAMS AND ALGEBRA

EXAMPLE 3: PARALLELOGRAMS AND COORDINATE GEOMETRY

Find the midpoint of MP. Find the midpoint of NR. EXAMPLE 3:

Given: ABCD Prove:  AED   BEC StatementsReasons 1. ABCD1. _______________________ 2. AE  CE and 2. _______________________ BE  DE 3. AD  BC3. _______________________ 4.  AED   BEC4. _______________________ EXAMPLE 4: PROOFS USING PROPERTIES OF PARALLELOGRAMS

p #9-14 all, evens, evens, all, 38, 46 Proofs:24-28 evens on handout 6.2 ASSIGNMENT