Name: _________________________________________________________ Date: _______________ Block: ________
Chapter 8
Properties of Parallelograms
Parallelograms
Rhombuses
Rectangles
SIDES AND ANGLES:
Both pairs of opposite sides are parallel
Both pairs of opposite angles are congruent
Both pairs of opposite sides are
Consecutive angles are supplementary
congruent
Both pairs of opposite sides are
Both pairs of opposite angles are congruent
congruent
Consecutive angles are supplementary
Both pairs of opposite sides are parallel
All sides are congruent
Both pairs of opposite sides are
Both pairs of opposite angles are congruent
congruent
Consecutive angles are supplementary
Both pairs of opposite sides are parallel
All angles are congruent.
Squares
Both pairs of opposite sides are
Both pairs of opposite angles are congruent
congruent
All angles are congruent.
Both pairs of opposite sides are parallel
Consecutive angles are supplementary
All sides are congruent
Ex. 1 List 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.
Ex. 2 Find the value of x:
a)
d) All sides are congruent.
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
Name: _________________________________________________________ Date: _______________ Block: ________
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
0
Ex. 1: ABCDBis an isosceles trapezoid
C and mB = 153 . Ex. 2: If diagonal AC is 2x – 3 and diagonal BD is 41 – 6x, find
the value for x and the measure of each diagonal.
o
153
A
A
B
D
D
.
C
Special Quadrilaterals
Directions: Place an “X” in the box for which each characteristic is true
Parallelogram
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
Rectangle
Rhombus
Square
Kite
Trapezoid
Isosceles
Trapezoid