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Chapter 6 Lesson 1

Chapter 6 Lesson 1. Classifying Quadrilaterals. Warm-up. Find the distance between the points to the nearest tenth. 1) M (2, -5) and N (-7,1) 2) P (-1, -3) and Q (-6, -9) 3 ) C (-4,6) and D(5, -3) Find the slope of the line through each pair of points.

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Chapter 6 Lesson 1

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  1. Chapter 6 Lesson 1 Classifying Quadrilaterals

  2. Warm-up • Find the distance between the points to the nearest tenth. 1) M (2, -5) and N (-7,1) 2) P (-1, -3) and Q (-6, -9) 3) C (-4,6) and D(5, -3) • Find the slope of the line through each pair of points. 4) X (0,6) and Y (4,9) 5) R (3,8) and S(6,0) 6) A (4,3) and B(2,1) 10.8 7.8 12.7 ¾ -8/3 1

  3. Special Quadrilaterals • Parallelogram • A quadrilateral with both pairs of opposite sides parallel.

  4. Rhombus • A parallelogram with four congruent sides.

  5. Rectangle • A parallelogram with four right angles

  6. Square • A parallelogram with four congruent sides and four right angles.

  7. Kite • A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. • If the shape is convex we call it a “dart”

  8. Trapezoid • A quadrilateral with EXACTLY one pair of parallel sides.

  9. Isosceles Trapezoid • A trapezoid in which non parallel opposite sides are congruent.

  10. Relationships among Quadrilaterals

  11. Example 1: Classifying a Quadrilateral • Classify DEFG as many ways as possible. • Quadrilateral • Parallelogram • Rectangle

  12. Your Turn! • How many ways can you classify WXYZ? • Quadrilateral • Parallelogram • Rhombus

  13. Classifying by Coordinate Methods • Determine the most precise name for quadrilateral LMNP. • Find the slope of each side • Are any sides parallel? 2) Use the distance formula to See if any pairs of sides are congruent. What is the most precise classification? Rhombus!

  14. Your Turn! • Determine the most precise name for quadrilateral ABCD with vertices A(-3,3), B(2,4), C(3,-1) and D(-2,-2) Square

  15. Using the Properties of Special Quadrilaterals Find the values of the variables for the kite. 2x + 4 = 3x – 5 -2x -2x 4 = x – 5 +5 +5 9 = x Substitute x = 9 into the equation: 2y + 5 = x + 6 2y + 5 = 15 2y = 10 Y = 5

  16. Your turn! • Find the values of each variable. Then find the length of each side. 2x + 2 = 4 2x = 2 X = 1 4, 2, 4, 7

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