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

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


The following quadrilaterals have opposite angles that are bisected:

  • Rhombus

  • Square


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 following quadrilaterals have congruent diagonals

  • Rectangle

  • Square

  • Isosceles Trapezoid


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.


  • 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

  • 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

B

D

C

A

Find x.


The following quadrilaterals have exactly one pair of opposite congruent angles

  • Kite


Example: Find the measures of the numbered angles.

46°

1

2

3


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.


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 bases

  • Its length is ½ the sum of the bases

MN || BC

MN || AD

MN = ½(BC+AD)


Find the following:

EF:

86°

3

4

108°


Find x:

x

8

12


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