1. 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)

2. Name that Quadrilateral
Example 2
What is the most specific name for the figure?
(Square) A B D C

3. 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.

4. 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.

5. 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

6. EXAMPLE 5
Identify a quadrilateral
Is enough information given in the diagram to show that quadrilateral PQRS is an isosceles trapezoid? Explain.
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.

7. 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

8. 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.

9. 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.

10. GUIDED PRACTICE
Example 8
Give the most specific name for the quadrilateral. Explain your reasoning.
ANSWER
Trapezoid: there is one pair of parallel sides.

11. 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.

12. Classify the Quadrilateral
Example 10
A(3,5) B(7,6) C(6,2) D(2,1)
(rhombus)