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Understanding Quadrilaterals: Properties, Types, and Theorems Explained

This chapter covers the essential properties and types of quadrilaterals, which are closed geometric figures with four sides and vertices. It introduces the concept of diagonals, the sum of interior angles, and focuses on specific types of quadrilaterals like parallelograms, rectangles, rhombi, and trapezoids. Key theorems are presented, highlighting characteristics such as congruent sides and angles, parallelism, and bisection of diagonals. The relationships between different quadrilaterals are illuminated, providing a comprehensive framework for understanding these geometric shapes.

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Understanding Quadrilaterals: Properties, Types, and Theorems Explained

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  1. Chapter 8 Quadrilaterals

  2. Section 8-1 Quadrilaterals

  3. A closed geometric figure with four sides and four vertices. Quadrilateral

  4. Any two sides, vertices, or angles of a quadrilateral are either consecutive or nonconsecutive.

  5. Segments whose endpoints are nonconsecutive vertices of a quadrilateral Diagonals

  6. The sum of the measures of the angles of a quadrilateral is 360°. Theorem 8-1

  7. Section 8-2 Parallelograms

  8. A quadrilateral with two pairs of parallel sides Parallelogram

  9. Opposite angles of a parallelogram are congruent. Theorem 8-2

  10. Opposite sides of a parallelogram are congruent. Theorem 8-3

  11. The consecutive angles of a parallelogram are supplementary. Theorem 8-4

  12. The diagonals of a parallelogram bisect each other. Theorem 8-5

  13. The diagonal of a parallelogram separates it into two congruent triangles. Theorem 8-6

  14. Section 8-3 Tests for Parallelograms

  15. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 8-7

  16. If one pair of opposite sides of a quadrilateral is parallel and congruent, then the quadrilateral is a parallelogram. Theorem 8-8

  17. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 8-9

  18. Section 8-4 Rectangles, Rhombi, & Squares

  19. A parallelogram with 4 right angles Rectangle

  20. A parallelogram with 4 congruent sides Rhombus

  21. A parallelogram with 4 congruent sides and 4 right angles Square

  22. The diagonals of a rectangle are congruent Theorem 8-10

  23. The diagonals of a rhombus are perpendicular Theorem 8-11

  24. Each diagonal of a rhombus bisects a pair of opposite angles Theorem 8-12

  25. Section 8-5 Trapezoids

  26. A quadrilateral with one pair of parallel sides Trapezoid

  27. The parallel sides are called bases • The nonparallel sides are called legs Bases and Legs

  28. Each trapezoid has two pairs of base angles Base Angles

  29. The segment that joins the midpoints of its legs Median

  30. The median of a trapezoid is parallel to the bases, and the length of the median equals one-half the sum of the lengths of the bases. Theorem 8-13

  31. Each pair of base angles in an isosceles trapezoid is congruent. Theorem 8-14

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