Properties of Other QuadrilateralsStudents will be able to…• Identify and use the

properties of rectangles, squares, rhombuses, kites, and trapezoids

The following quadrilaterals have perpendicular diagonals:Rhombus Square Kite

The following quadrilaterals have opposite angles that are bisected: Rhombus Square

Example: Find the measures of the numbered angles in the rhombus.

1

2

3 4

12°

The figure below is a rhombus. Find TQ, TP, and SQ.

The following quadrilaterals have congruent diagonals

Rectangle Square Isosceles Trapezoid

EQSR

EXAMPLE

BD=5y-7 and AC = y + 5. Find the value of y and the length of BE.

E

EXAMPLE:If BD= 2x+10 and AC=x+15, find x and the length of the diagonals.

TRAPEZOID

LEGLEG

BASE ANGLES

BASE ANGLES

•The 2 parallel sides are the bases•The 2 non-parallel sides are the legs

A

B

C

D

Name the following:Bases:

Legs:

2 Pairs of Base Angles:

The following quadrilaterals have exactly one pair of opposite parallel sides

•Trapezoid•Isosceles Trapezoid

The following quadrilaterals have exactly one pair of opposite congruent sides:

•Isosceles Trapezoid

Theorem:

The base angles of an isosceles trapezoid are congruent

A

B

C

D

DB

CA

21

3

xCm

xAm

Example- Find x given the following angle measures:

The following quadrilaterals have exactly one pair of opposite congruent angles

Kite

Example: Find the measures of the numbered angles.

46°

3

2

1

44° 112°

1

2

FIND THE MEASURE OF THE MISSING ANGLES.

, assign x to represent each measure. So equation will be:

44+112+x+x = 360

How many degrees in a quadrilateral?

What do we know about the relationship between angles 1 and 2?

21 mm

2 angles that share a leg in a trapezoid are supplementary because they are same-side interior angles.

180 CmAm

The following is an isosceles trapezoid. The measure of angle A= 110. Find the measures of the other 3 angles.

Midsegment (Median) of a Trapezoid

Joins the midpoints of the nonparallel sides

Is parallel to the basesIts length is ½ the sum of the bases

MN || BC

MN || AD

MN = ½(BC+AD)

4

386°

108°

Find the following:EF:

:

:

:

:

:

AB

DF

DCBm

CFEm

BADm

Find x:

8

12

x