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)

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

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 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.

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)