8.6 Examples

• Example 1• STUV has at least one pair of consecutive sides

that are congruent. What type of quadrilateral meets this condition?

• (rhombus, square, or kite)

• Example 2• What is the most specific name for the figure?

• (Square)

A B

CD

Name that Quadrilateral

EXAMPLE 3 Identify quadrilaterals

Quadrilateral ABCD has at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition?

SOLUTION

There are many possibilities.

EXAMPLE 4 Standardized Test Practice

SOLUTION

The diagram shows AE CE and BE DE . So, the diagonals bisect each other. By Theorem 8.10, ABCD is a parallelogram.

EXAMPLE 4 Standardized Test Practice

Rectangles, rhombuses and squares are also parallelograms. However, there is no information given about the side lengths or angle measures of ABCD. So, you cannot determine whether it is a rectangle, a rhombus, or a square.

The correct answer is A.

ANSWER

EXAMPLE 5

SOLUTION

STEP 1

Show that PQRS is a trapezoid. R and S are supplementary, but P and S are not. So, PS QR , but PQ is not parallel to SR . By definition, PQRS is a trapezoid.

Identify a quadrilateral

Is enough information given in the diagram to show that quadrilateral PQRS is an isosceles trapezoid? Explain.

EXAMPLE 5 Identify a quadrilateral

STEP 2

Show that trapezoid PQRS is isosceles. P and S are a pair of congruent base angles. So, PQRS is an isosceles trapezoid by Theorem 8.15.

Yes, the diagram is sufficient to show that PQRS is an isosceles trapezoid.

ANSWER

GUIDED PRACTICE Example 6

Quadrilateral DEFG has at least one pair of opposite sides congruent. What types of quadrilaterals meet this condition?

ANSWER

Parallelogram, Rectangle, Square, Rhombus, Trapezoid.

GUIDED PRACTICE Example 7

Give the most specific name for the quadrilateral.Explain your reasoning.

ANSWER

Kite: there are two pairs of consecutive congruent sides.

GUIDED PRACTICE Example 8

Give the most specific name for the quadrilateral.Explain your reasoning.

ANSWER

Trapezoid: there is one pair of parallel sides.

GUIDED PRACTICE Example 9

Give the most specific name for the quadrilateral.Explain your reasoning.

ANSWER

Quadrilateral; there is not enough information to be more specific.

Classify the Quadrilateral

• Example 10

• A(3,5) B(7,6) C(6,2) D(2,1)

• (rhombus)