Unit 7: Quadrilaterials

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Presentation transcript:

Unit 7: Quadrilaterials 6-1, 6-2 Classifying Quads, Properties of parallelograms

Warm Up 4/16/13 Be sure you have copied down the definitions from your homework. If not, take this time to do so as we won’t have time during class Review your definitions

Unit 7 Essential Questions How can I use the relationships of sides, angles, and diagonals of parallelograms to solve problems? How can I use properties of all quadrilaterals to solve problems?

Bonus Question See website

Agenda Warm Up 6-1: Classifying Quadrilaterals 6-2: Properties of Parallelograms Classwork/Homework

Today’s Objective Students will be able to define and classify special types of quadrilaterals. Students will be able to use relationships among sides and angles of parallelograms Students will be able to use relationships involving diagonals of parallelograms or transversals.

6-1: Classifying Quadrilaterals Polygon with 4 sides. Name it going around it. EX: ABCD or BCDA B A D C

Parallelogram Definition: A Parallelogram is a quadrilateral with two pairs of parallel sides (Opposite sides are parallel) Symbol:

Rhombus Definition: A Rhombus is a parallelogram with four congruent sides.

Rectangle Definition: A Rectangle is a parallelogram with four right angles

Square Definition: A Square is a parallelogram with four congruent sides and four right angles

Kite Definition: A Kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

Trapezoid Definition: A Trapezoid is a quadrilateral with exactly one pair of parallel sides.

Isosceles Trapezoid Definition: An Isosceles Trapezoid is a trapezoid whose nonparallel opposite sides are congruent

6-2: Properties of Parallelograms Review: A Parallelogram is a quadrilateral with two pairs of parallel sides (Opposite sides are parallel) Symbol:

Other Properties of a 1. Opposite sides are

2. Opposite ∠ ‘s are ∠

Same side interior angles 3. Consecutive ∠ ‘s are supplementary (Sum to 180) a+b = 180 b+d=180 a+c=180 c+d=180 Same side interior angles

4. Diagonals bisect each other (cut in half)

Example 1: ABCD is a AB = 5x+3, DC=4x+15. Find x

Ex 2: m<ADC = 68 Find m<DCB Find m<CBA Find m<BAD

Ex.3: AE=2x+5, EC=4x-9, Find AC

Ex. 4: DB=8x-4, EB=2x, Find DE

Homework Left side of page 2 of packet For extra practice, attempt proofs on right side