Chapter 6

Quadrilaterals

6.1 Classifying Quadrilaterals

Parallelograms– Both pairs of opposite sides are parallel

Rhombus– Four congruent sides

Rectangle– Four right angles

Square– Four congruent sides and four congruent angles

Kite– Two pairs of adjacent sides congruent and no opposite sides congruent

Trapezoid – Exactly one pair of parallel sides

Isosceles Trapezoid– Nonparallel sides are congruent

Classifying Quadrilaterals

1. Is a square always a rectangle?

Classifying Quadrilaterals

2. Is a rectangle always a square?

Classifying Quadrilaterals

3. Is a square always a rhombus?

Classifying Quadrilaterals

4. Is a rhombus always a square?

Classifying Quadrilaterals

5. Is a square always parallelogram?

Classifying Quadrilaterals

6. Is a kite always parallelogram?

Classifying Quadrilaterals

7. Are there any shapes that are always parallelograms?

Classifying Quadrilaterals

Make a concept map Include all quadrilaterals

– Provide pictures, definitions, or key information needed to link the quadrilaterals

Quadrilaterals

Kite

Trapezoid

Isosceles Trapezoid

Parallelogram

Rectangle

Square

Rhombus

Using properties of special quadrilaterals

6x

42 x 53 x

52 y

J

T

K

B

•Find the values of the variables for the kite. Then find the length of each side.

You try

Find the values of the variables.

x= _________,y=_____________

Assignment

Worksheet and Pg 309 1-24

6.2 Properties of Parallelograms

What do you think the properties of a parallelogram are? Sides? Angles?

Prove opposite sides of a parallelogram are congruent

Given: ABCD is a Parallelogram Prove:

AB CD, BC DA

A

B C

D

Properties of Parallelograms

6-1 Opposite sides of a parallelogram are congruent.

6-2 Opposite angles of a parallelogram are congruent

Consecutive angles of a parallelogram are supplementary

Diagonals of a Parallelogram

Properties of parallelogram 6.2.gsp

Theorem 6-3– The diagonal of a parallelogram bisect each

other.

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.

BD DF

Assignment

H:\Geometry\lessons\Chapter 6.ppt Pg 315, 1-41 odd

6.3 Proving that a Quadrilateral is a Parallelogram

text book site If both pairs of opposite sides of a

quadrilateral are congruent, then the quadrilateral is a parallelogram.

If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.

More Theorems

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

If one pair of opposites sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Assignment

Pg 324, 1-10

6.4 Special Parallelograms

– Properties of Rhombuses 6.4.gsp

6-9 Each diagonal of a rhombus bisects two angles of the rhombus.

6-10 The diagonals of a rhombus are perpendicular.– Diagonals of a Rectangle 6.4.gsp

6-11 The diagonals of a rectangle are congruent.

Is the parallelogram a rhombus or a rectangle?

6-12 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.

6-13 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

6-14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Assignment

Pg 332, 1-17 odd 25-34 all

6.5 Trapezoids and Kites

Trapezoids– 6-15 The base angles of an isosceles trapezoid

are congruent.

– 6-16 The diagonals of an isosceles trapezoid are congruent.

Kites

6.5 Kite.gsp

6-17 The diagonals of a kite are perpendicular.

Assignment

Pg 338, 1-6 all, 8-16 even