leq: how do we classify and use properties of quadrilaterals?

Warmup: True or false: all rhombi are squares. Once warmup is completed, grab a note sheet and copy chart.

Chapter 6.1: Classifying

QuadrilateralsLEQ: How do we classify and use properties

of quadrilaterals?

A quadrilateral is a 4-sided polygon.

Box #1: “Quadrilateral”

“a quadrilateral with 2 pairs of congruent adjacent sides and no congruent opposite sides.”

No parallel sides

Box #2: “Kite”

“a quadrilateral with exactly one pair of parallel sides.”

Box #4: “Isosceles trapezoid”◦ Trapezoid who’s nonparallel opposite sides are

congruent.

Box #3: “Trapezoid”

“a quadrilateral with exactly 2 pairs of opposite parallel sides.

Why would the definition of trapezoid say “exactly one” pair of parallel opposite sides?

Box #5: “Parallelogram”

A parallelogram with a right angle.

Book definition “4 right angles.” Why don’t we need to say all four angles are 90 degrees?

Box #6: “Rectangle”

A parallelogram with 4 congruent sides.

Box #7: “Rhombus”

A parallelogram with 4 congruent sides and a right angle.

Book defn. “4 right angles”

Box #8: Square

“most precise”-means “most specific” aka lowest possible place on the chart.

Ex. A.) What is the most specific name for the figure below? B.) list all names that apply

Keep in mind: you may have to use coordinate plane to identify most precise name.

“most precise” vs. “all names that apply”

6.2 Properties of Parallelograms

LEQ: What are the properties of parallelograms?

3 Theorems Opposite sides are congruent Opposite angles are congruent The diagonals of a parallelogram bisect

each other

Thm. 6.1Why should the opposite sides of a

parallelogram be congruent?In the triangles below, prove AC=DB and AD=BCStatements Reasons

1.) m<1=m<2 1.) Alt. int. angles

3.) Reflexive3.) AB=AB

2.) “ “2.) m<3=m<4

4.)ABCBAD 4.) ASA

5.) AC=DB 5.) CPCTC

6.) “ “6.) AD=BC

1

D

C

B

A

4

3

2

Theorem 6-4

If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Example

In the figure at the right, DH || CG, BF || AE, AB = BC = CD = 2 and EF = 2.5. Find EH.

A

FB

HD

E

GC