Notes: Quadrilaterals

Properties of Quadrilaterals

four sides

angles add to 360°

Properties of Parallelograms

same as Quadrilaterals

opposite sides and congruent and parallel

opposite angles are congruent

diagonals bisect each other

consecutive angles are supplementary

Properties of Rectangles

same as Parallelograms

four 90° angles

diagonals are congruent

GEOMETRY 9

NOTES Date: _______________

__________________________________________________________

Isosceles

Trapezoids

Parallelograms Non-Parallelograms

Rectangles Kites

Always

Sometimes

Never Squares

Rhombi

Quadrilaterals

Trapezoids

Properties of Rhombi

same as Parallelograms

diagonals are perpendicular to each other

all sides are congruent

Properties of Squares

same as Rectangles and Rhombi

We may use properties of quadrilateral to write algebraic equations and solve for

missing variables.

Examples: Solve for the missing variables in each of the following parallelograms.

(14𝑥 + 18)°

(10𝑥 − 30)°

𝑦°

𝑧°

56 feet

42 feet 𝑥 feet

Learning Check: Solve for the missing variables in each of the following

parallelograms.

𝐴𝐶̅̅ ̅̅ = 18

𝐵𝐷̅̅ ̅̅ = 24

Perimeter = _________

288 cm

(𝑥 − 124) cm

D C

A B

4𝑥 − 37

2𝑥 + 1

2𝑥 + 100

7𝑥 + 10

14

Perimeter = _________

𝐴𝐶̅̅ ̅̅ = 45

𝐵𝐷̅̅ ̅̅ = 60

Perimeter = _________

D C

A B

NON-PARALLELOGRAMS

Properties of Trapezoids

one pair of opposite sides are parallel

- two parallel sides are called bases

- the nonparallel sides are called legs

Properties of Isosceles Trapezoids

has one pair of congruent sides

congruent diagonals

base angles are congruent

Properties of Kites

two distinct pairs of adjacent congruent sides

Examples: Use the properties of non-parallelograms to write equations and solve

for the missing variables.

Learning Check: Use the properties of non-parallelograms to write equations and

solve for the missing variables.

45°

(2𝑥 + 15)°

8𝑥 + 100

75° 3𝑦° 90°

2𝑥°

15𝑥 − 40

A B

C D

100°

x°