Properties of Other Quadrilaterals Students will be able to… Identify and use the properties of...

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