More Quadrilaterals - Trapezoids and Kites

More Types of Quadrilaterals

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Parallelograms

Trapezoids

Another type of quadrilateral that is NOT in the parallelogram family is the trapezoid.

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

Multiple Choice

What is the angle relationship name for angles 1 and 2?

• Corresponding

• Alternate Interior

• Same Side Interior

• Vertical

Same Side Interior Angles

Angles 1 and 2 are same side interior angles. They are on the same side of a transversal, between two parallel lines.

Use your angle relationships resource page to learn more about this relationship!

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

Same Side Interior Angles

Because there is just one pair of parallel lines, the only other supplementary same side interior angles are 3 and 4.

So Angle 1 + Angle 2 = 180, and Angle 3 + Angle 4 = 180.

Answer: x=12

Diagonals of a Trapezoid

For most trapezoids, there are no special properties about the diagonals.

Some types of trapezoids have congruent diagonals, which we'll see later.

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

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

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.

• 115

• 93

• 98

• 110

Answer: x=70

All angles add to 360°

Solving the equation

gives the answer x = 70.

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 $$m\angle T$$  

• 40.5

• 43

• 81

• 119

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 x.

• 7.5

• 8

• 11

• 15

Multiple Choice

Use the markings to determine the name of the quadrilateral.

• Rectangle

• Square

• Trapezoid

• Kite

Answer: Kite

Although it was drawn to look like a square, the markings tell us that this shape has two pairs of adjacent congruent sides and one pair of congruent angles.

So it must be a kite.

Multiple Choice

Use the markings to determine the name of the quadrilateral.

• Rectangle

• Parallelogram

• Isosceles Trapezoid

• Kite

Correct Answer: Isosceles Trapezoid

According to the diagram, the figure has only one pair of parallel sides, plus base angles that are congruent.

Therefore it must be an isosceles trapezoid.