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Bell Ringer

Bell Ringer. Special Quadrilaterals . Example 1. Use Properties of Quadrilaterals. Determine whether the quadrilateral is a trapezoid, parallelogram, rectangle, rhombus, or square. SOLUTION.

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Bell Ringer

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  1. Bell Ringer

  2. Special Quadrilaterals

  3. Example 1 Use Properties of Quadrilaterals Determine whether the quadrilateral is a trapezoid, parallelogram, rectangle, rhombus, or square. SOLUTION The diagram shows CEEA and DEEB, so the diagonals of the quadrilateral bisect each other. By Theorem 6.9, you can conclude that the quadrilateral is a parallelogram. You cannot conclude that ABCD is a rectangle, rhombus, or square because no information about the sides or angles is given.

  4. Example 2 Identify a Rhombus Are you given enough information in the diagram to conclude that ABCD is a square? Explain your reasoning. SOLUTION The diagram shows that all four sides are congruent. Therefore, you know that it is a rhombus. The diagram does not give any information about the angle measures, so you cannot conclude that ABCD is square.

  5. Example 3 SOLUTION 1. First show that EFGH is a trapezoid. E and F are supplementary, so FG is parallel to EH by Theorem 3.10, the Same-Side Interior Angles Converse. So, EFGH has at least one pair of parallel sides. Identify a Trapezoid Are you given enough information in the diagram to conclude that EFGH is an isosceles trapezoid? Explain your reasoning. 2. Next show that EFGH is isosceles. Because the base angles are congruent,EFGH is an isosceles trapezoid by Theorem 6.13. To show that EFGH is a trapezoid, you must show that it has only one pair of parallel sides. The opposite angles of EFGH are not congruent, so it cannot be a parallelogram. Therefore, EFGH is a trapezoid.

  6. Now You Try  Identify Quadrilaterals Are you given enough information to conclude that the figure is the given type of special quadrilateral? Explain your reasoning. 1. A square? ANSWER No; all four angles are right angles, so the figure is a rectangle. There is no information about the sides, so you cannot conclude that PQRS is a square.

  7. Identify Quadrilaterals Now You Try  Are you given enough information to conclude that the figure is the given type of special quadrilateral? Explain your reasoning. 2. A rhombus? ANSWER No; both pairs of opposite angles are congruent, so the figure is a parallelogram. There is no information about the sides, so you cannot conclude that WXYZ is a rhombus.

  8. ANSWER || Yes; L and M are supplementary, so KL JM by the Same-Side Interior Angles Converse. Since J and M are not supplementary, KJ is not parallel to LM. The figure has exactly one pair of parallel sides, so it is a trapezoid. Now You Try  Identify Quadrilaterals Are you given enough information to conclude that the figure is the given type of special quadrilateral? Explain your reasoning. 3. A trapezoid?

  9. Now You Try 

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  13. Page 337

  14. Complete Pages 339-341#s 2-26 even only

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