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EXAMPLE 1

EXAMPLE 1. 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.

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EXAMPLE 1

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  1. EXAMPLE 1 Identify quadrilaterals Quadrilateral ABCDhas at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition? SOLUTION There are many possibilities.

  2. The diagram shows AE CEand BE DE. So, the diagonals bisect each other. By Theorem 8.10, ABCD is a parallelogram. EXAMPLE 2 Standardized Test Practice SOLUTION

  3. The correct answer is A. ANSWER EXAMPLE 2 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.

  4. Is enough information given in the diagram to show that quadrilateral PQRSis an isosceles trapezoid? Explain. STEP 1 Show that PQRSis a trapezoid. Rand Sare supplementary,but P and S are not. So, PS QR , but PQis not parallel to SR. By definition, PQRSis a trapezoid. EXAMPLE 3 Identify a quadrilateral SOLUTION

  5. STEP 2 Show that trapezoid PQRS is isosceles. P and Sare a pair of congruent base angles. So, PQRSis an isosceles trapezoid by Theorem 8.15. ANSWER Yes, the diagram is sufficient to show that PQRS is an isosceles trapezoid. EXAMPLE 3 Identify a quadrilateral

  6. ANSWER Parallelogram, Rectangle, Square, Rhombus, Trapezoid. In all these quadrilaterals at least one pair of opposite sides is congruent. for Examples 1, 2 and 3 GUIDED PRACTICE 1. Quadrilateral DEFGhas at least one pair of opposite sides congruent. What types of quadrilaterals meet this condition?

  7. ANSWER It is a kite as kite is a quadrilateral that has two pair of consecutive congruent sides, but opposite sides are not congruent. for Examples 1, 2 and 3 GUIDED PRACTICE Give the most specific name for the quadrilateral.Explain your reasoning.

  8. ANSWER VWXY is a trapezoid. one pair of opposite sides are parallel, and the diagonals do not bisect each other, therefore it is a trapezoid. for Examples 1, 2 and 3 GUIDED PRACTICE Give the most specific name for the quadrilateral.Explain your reasoning.

  9. ANSWER Quadrilateral; there is not enough information to be more specific. for Examples 1, 2 and 3 GUIDED PRACTICE Give the most specific name for the quadrilateral.Explain your reasoning.

  10. ANSWER MNPQ could be a rectangle or a square since you do not know the relationship between MQ and NP. There is not enough information to conclude it is an isosceles trapezoid. 5. Error AnalysisA student knows the following information about quadrilateral MNPQ:MN PQ ,MP NQ , and P Q. The student concludes that MNPQis an isosceles trapezoid. Explain why the student cannot make this conclusion. for Examples 1, 2 and 3 GUIDED PRACTICE

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