Name: ______Date: ______Block: ______

Chapter 8

Properties of Parallelograms

SIDES AND ANGLES:

Parallelograms / Both pairs of opposite sides are parallel
Both pairs of opposite sides are congruent / Both pairs of opposite angles are congruent
Consecutive angles are supplementary
Rhombuses / Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
All sides are congruent / Both pairs of opposite angles are congruent
Consecutive angles are supplementary
Rectangles / Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel / Both pairs of opposite angles are congruent
Consecutive angles are supplementary
All angles are congruent.
Squares / Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
All sides are congruent / Both pairs of opposite angles are congruent
All angles are congruent.
Consecutive angles are supplementary

Ex. 1List the quadrilaterals for which the statements are true:

a) Both pairs of opposite sides are parallel. b) Both pairs of opposite sides are congruent.

c) All angles are congruent. d) All sides are congruent.

Ex. 2 Find the value of x:

a) b) c)

DIAGONALS

Parallelograms /
The diagonals bisect each other
Rhombuses / The diagonals bisect the angles
The diagonals are perpendicular
The diagonals bisect each other
Rectangles /
The diagonals are congruent
The diagonals bisect each other
Squares / The diagonals are congruent
The diagonals bisect the angles
The diagonals are perpendicular
The diagonals bisect each other

Ex. 3 List the quadrilaterals for which the statements are true.

a) The diagonals are congruent.b) The diagonals bisect the angles. c) The diagonals are perpendicular

Kites and Trapezoids

If a trapezoid is isosceles…
*The bases of the trapezoid are parallel *opposite sides are congruent
*base angles are congruent *diagonals are congruent
*adjacent angles (not base angles)are supplementary

Ex. 1: ABCD is an isosceles trapezoid and mB = 1530. Ex. 2: If diagonal AC is 2x – 3 and diagonal BD is 41 – 6x, find

the value for xand the measure of each diagonal.

.

Special Quadrilaterals

Directions: Place an “X” in the box for which each characteristic is true

Parallelogram / Rectangle / Rhombus / Square / Kite / Trapezoid
/ Isosceles Trapezoid
Figure with four sides
Angles add to 360
All s are 
Both pairs of opposite s 
Only one pair of opposite s are 
All sides are 
Both pairs of opposite sides are 
Both pairs of opposite sides are ||
Only one pair of|| opposite sides
Diagonals are 
Diagonals are 
Diagonals bisect angles at vertex
Diagonals bisect each other