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Exploring Special Quadrilaterals: Definitions and Classifications

Learn how to define and classify parallelograms, rhombuses, rectangles, squares, kites, and trapezoids. Practice judging and determining special quadrilaterals using coordinate methods. Solve for variables in special quadrilaterals like kites and rhombuses.

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Exploring Special Quadrilaterals: Definitions and Classifications

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  1. Chapter 6 Lesson 1 Objective: To define and classify special types of quadrilaterals.

  2. Classifying Special Quadrilaterals Definitions:   A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles are supplementary. A rhombus is a parallelogram with four congruent sides.

  3. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles. A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.

  4.  A trapezoid is a quadrilateral with exactly one pair of parallel sides. The isosceles trapezoid at the bottom is a trapezoid whose nonparallel opposite sides are congruent.

  5. Example 1: Classifying Quadrilaterals Judging by appearance, classify DEFG in as many ways as possible. Explain. DEFG is a quadrilateral because it has four sides. It is a parallelogram because both pairs of opposite sides are parallel. It is a rectangle because it has four right angles.

  6. Example 2: Classifying Quadrilaterals Judging by appearance, classify ABCD in as many ways as possible. B C A D Quadrilateral Trapezoid

  7. Special Quadrilaterals

  8. Example 3: Classifying by Coordinate Methods Determine the most precise name for quadrilateral LMNP. Step 1: Find the slope of each line. • Slope of LM = • Slope of NP = • Slope of MN = • Slope of LP = Slope Formula

  9. Example 3: (cont.) Both pairs of opposite sides are parallel, so LMNP is a parallelogram. No sides are perpendicular, so LMNP is not a rectangle. Step 2: Use the distance formula All sides are congruent, so LMNP is a rhombus.

  10. Example 4: Using the Properties of Special Quadrilaterals Find the values of the variables for the kite.

  11. Example 5: Using the Properties of Special Quadrilaterals Find the values of the variables for the rhombus. Then find the lengths of the sides. 3b + 2 L N 5a + 4 3a + 8 S T 4b - 2

  12. Assignment Page 290-291 #1-26

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