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

Properties of Other Quadrilaterals

Students will be able to…

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




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

1

12°

2

4

3



The following quadrilaterals have congruent diagonals
The following quadrilaterals have congruent diagonals bisected:

  • Rectangle

  • Square

  • Isosceles Trapezoid


Example
EXAMPLE bisected:

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

E


EXAMPLE: bisected:

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


Trapezoid

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: opposite parallel sides

The base angles of an isosceles trapezoid are congruent

B

D

C

A

Find x.



Example find the measures of the numbered angles
Example: opposite congruent anglesFind the measures of the numbered angles.

46°

1

2

3


1 opposite congruent angles

44°

112°

2

FIND THE MEASURE OF THE MISSING ANGLES.




Midsegment median of a trapezoid
Midsegment 3 angles. (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)


Find the following: 3 angles.

EF:

86°

3

4

108°


Find x
Find x: 3 angles.

x

8

12


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