Name: ______Date: ______Block: ______
Chapter 8
Properties of Parallelograms
SIDES AND ANGLES:
Parallelograms / Both pairs of opposite sides are parallelBoth 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 mB = 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