6.6 Trapezoids and Kites

Are all quadrilaterals parallelograms?

Parallelograms

Trapezoids

A trapezoid is a type of quadrilateral with only one pair of parallel sides.

Multiple Choice

Can you find the trapezoid in the parallel lines? What is the angle relationship name for angles 1 and 2?

• Corresponding

• Alternate Interior

• Same Side Interior

• Vertical

Fill in the Blanks

If  $m\angle1$   $=105\degree$  

then  $m\angle2=$  

$\degree$  

Multiple Select

Are there any other supplementary same side interior angles in the diagram? Select all that apply.

• 2 and 3

• 3 and 4

• 1 and 4

Multiple Select

Select all of the properties below that are true about ALL trapezoids.

• Pair of parallel sides

• Pair of congruent sides

• Two pairs of supplementary angles

• Two pairs of congruent angles

• Congruent diagonals

Isosceles Trapezoid

• Much like an Isosceles triangle, an isosceles trapezoid has two congruent sides

• The congruent sides will ALWAYS be the non parallel sides

• Look for the congruent markings to know that a trapezoid is isosceles

Isosceles Trapezoid

• An isosceles trapezoid has a few more unique properties...

• "Base" angles are congruent (A and D; B and C)

• Diagonals are congruent

Fill in the Blanks

Find

$m\angle D$ . $m\angle D=$  

$\degree$  

Multiple Choice

Select the correct values of x and y

• x=56, y=56

• x=56, y=124

• x=124, y=56

• x=124, y=124

Multiple Select

Select all of the properties below that are true about Isosceles trapezoids.

• Pair of parallel sides

• Pair of congruent sides

• Two pairs of supplementary angles

• Two pairs of congruent angles

• Congruent diagonals

Midsegment of Trapezoids

Multiple Choice

Find $$x$$  

• 12

• 13

• 19

• 26

Remember!

Quadrilateral Angle Sum

If you add all of the angles in a quadrilateral, their sum will be 360°.

Use this property to help find missing angle measures!

Multiple Choice

Use the quadrilateral sum theorem to find the measure of ∠G.

• 105

• 100

• 75

• 80

Kites

• Quadrilateral ABCD at the right is a kite

• Kites have two pairs of congruent adjacent sides (congruent sides are next to each other)

• Kites also have ONE pair of congruent angles

• Kites are symmetric down the middle

Multiple Choice

Find $$m\angle A$$  

• 81

• 118

• 99

• 62

Fill in the Blanks

Find the measure of Angle A.

$m\angle A=$  

$\degree$  

Diagonals of a Kite

When the diagonals are drawn in a kite, they form four right angles. Therefore the diagonals of a kite are perpendicular.

One diagonal also bisects the other.

Multiple Choice

Find the value of 2x-7.

• 7.5

• 8

• 11

• 15

Multiple Choice

Use the markings to determine the name of the quadrilateral.

• Rectangle

• Rhombus

• Trapezoid

• Kite

Multiple Choice

Use the markings to determine the name of the quadrilateral.

• Trapezoid

• Parallelogram

• Isosceles Trapezoid

• Kite

Objective - 6.6 Trapezoids and Kites

To verify and use properties of trapezoids and kites.

Multiple Choice

Mario’s pool is in the shape of a quadrilateral. It has two congruent sides and the other two sides are parallel with each other. There are no right angles. Choose the most precise name for the shape of Mario’s pool.

• trapezoid

• isosceles triangle

• isosceles trapezoid

• kite