Properties of other quadrilaterals
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Properties of Other Quadrilaterals. Students 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.

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Properties of Other Quadrilaterals

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Properties of other quadrilaterals

Properties of Other Quadrilaterals

Students will be able to…

Identify and use the properties of rectangles, squares, rhombuses, kites, and trapezoids


The following quadrilaterals have perpendicular diagonals

The following quadrilaterals have perpendicular diagonals:

  • Rhombus

  • Square

  • Kite


The following quadrilaterals have opposite angles that are bisected

The following quadrilaterals have opposite angles that are bisected:

  • Rhombus

  • Square


Example find the measures of the numbered angles in the rhombus

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

1

12°

2

4

3


The figure below is a rhombus find tq tp and sq

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


The following quadrilaterals have congruent diagonals

The following quadrilaterals have congruent diagonals

  • Rectangle

  • Square

  • Isosceles Trapezoid


Example

EXAMPLE

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

E


Properties of other quadrilaterals

EXAMPLE:

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


Trapezoid

  • The 2 parallel sides are the bases

  • The 2 non-parallel sides are the legs

TRAPEZOID

BASE ANGLES

B

D

LEG

LEG

A

C

BASE ANGLES

Name the following:

Bases:

Legs:

2 Pairs of Base Angles:


The following quadrilaterals have exactly one pair of opposite parallel sides

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

Theorem:

The base angles of an isosceles trapezoid are congruent

B

D

C

A

Find x.


The following quadrilaterals have exactly one pair of opposite congruent angles

The following quadrilaterals have exactly one pair of opposite congruent angles

  • Kite


Example find the measures of the numbered angles

Example: Find the measures of the numbered angles.

46°

1

2

3


Properties of other quadrilaterals

1

44°

112°

2

FIND THE MEASURE OF THE MISSING ANGLES.


2 angles that share a leg are supplementary because they are same side interior angles

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


The measure of angle a 110 find the measures of the other 3 angles

The measure of angle A= 110. find the measures of the other 3 angles.


Midsegment median of a trapezoid

Midsegment (Median) of a Trapezoid

  • Joins the midpoints of the nonparallel sides

  • Is parallel to the bases

  • Its length is ½ the sum of the bases

MN || BC

MN || AD

MN = ½(BC+AD)


Properties of other quadrilaterals

Find the following:

EF:

86°

3

4

108°


Find x

Find x:

x

8

12


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