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6.6 Reasoning About Special Quadrilaterals

6.6 Reasoning About Special Quadrilaterals. Textbook page 337. What makes a quadrilateral a parallelogram?. Both pairs of opposite sides are parallel OR both pairs of opposite sides are congruent OR all pairs of consecutive angles are supplementary

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6.6 Reasoning About Special Quadrilaterals

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  1. 6.6 Reasoning About Special Quadrilaterals Textbook page 337

  2. What makes a quadrilateral a parallelogram? • Both pairs of opposite sides are parallel • OR both pairs of opposite sides are congruent • OR all pairs of consecutive angles are supplementary • OR both pairs of opposite angles are congruent • OR the diagonals bisect each other

  3. What makes a quadrilateral a rhombus? • is a parallelogram • AND all sides are congruent

  4. What makes a quadrilateral a rectangle? • is a parallelogram • AND has four congruent angles (900 each)

  5. What makes a quadrilateral a square? • is a parallelogram • AND has four congruent sides • AND has four congruent angles (900 each)

  6. What makes a quadrilateral a trapezoid? • EXACTLY ONE pair of parallel sides

  7. What makes a quadrilateral an isosceles trapezoid? • is a trapezoid • AND has congruent legs

  8. Quadrilaterals parallelogram trapezoid ordinary quadrilateral ordinary parallelogram rhombus rectangle ordinary trapezoid isosceles trapezoid square ordinary rhombus ordinary rectangle

  9. Examples on pg 338 • 1) no, all four angles are 900 so it is a rectangle, but there is no information about the sides, so you cannot conclude that PQRS is a square • 2) no, both pairs of opposite angles are congruent, so the figure is a parallelogram, but there is no information about the sides, so you cannot conclude that WXYZ is a rhombus • 3) yes, <L and <M are supplementary so KL and JM are parallel by same side interior angles converse, Since <J and <M are not supplemntary, KJ is not parallel to LM. The figure has exactly one pair of parallel sides, so it is a trapezoid.

  10. Homework • Assignment # 15 • Pg 339 • Problems 1-23 all, 26, 27-37 odd • Do not pack up before you are finished or you are told to do so by Mrs. Takayama

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