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Chapter 8

Chapter 8. Quadrilaterals. Quadrilaterals. 8-1. Quadrilaterals. 8-1. Objective: Identify parts of quadrilaterals and find the sum of the measures of the interior angles of a quadrilateral. Quadrilateral – a closed geometric figure with four sides and four vertices.

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Chapter 8

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  1. Chapter 8 Quadrilaterals

  2. Quadrilaterals 8-1

  3. Quadrilaterals 8-1 Objective: Identify parts of quadrilaterals and find the sum of the measures of the interior angles of a quadrilateral. Quadrilateral – a closed geometric figure with four sides and four vertices. Quadrilaterals Not Quadrilaterals

  4. Quadrilateral ABCD Quadrilateral BCDA Quadrilateral DCBA

  5. 90 + 90 + 50 + a = 360 230 + a = 360 a = 130

  6. 2x + 40 + 2x + 40 = 360 4x + 80 = 360 -80 -80 4x = 280 x = 70

  7. 8-2 Parallelograms

  8. Objective: Identify and use the properties of parallelograms. 8-2 Parallelograms Parallelogram – a quadrilateral with two pairs of parallel sides.

  9. 70° 15 20 SR = 20 SP = 15

  10. 70° 15 20

  11. 70° 20 20

  12. AE = ½ (AC) AE = ½ (56) AE = 28

  13. 8-3 Tests for Parallelograms

  14. 8-3 Tests for Parallelograms Objective: Identify and use tests to show that a quadrilateral is a parallelogram.

  15. 1. Alternate interior angles are congruent. 2. Reflexive 3. Given 4. SAS 5. CPCTC 6. Theorem 8-7

  16. No Yes; both pairs of opposite sides are congruent.

  17. > > Yes; diagonals bisect each other. Yes; one pair of opposite sides is congruent and parallel.

  18. Rectangles, Rhombi, and Squares 8-4

  19. Rectangles, Rhombi, and Squares 8-4 Objective: Identify and use the properties of rectangles, rhombi, and squares.

  20. XZ = 14

  21. 8-5 Trapezoids

  22. Objective: Identify and use the properties of trapezoids and isosceles trapezoids. 8-5 Trapezoids Trapezoid – a quadrilateral with exactly one pair of parallel sides.

  23. Bases AB and CD Legs AD and BC Base Angles

  24. 12 18 MN = ½ (12 + 18) MN = ½ (30) MN = 15

  25. 120° 120° 60°

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