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Chapter 6: Quadrilaterals

In this chapter on quadrilaterals, we explore special types of parallelograms, focusing on rhombuses and rectangles. Theorems highlight unique properties, such as how the diagonals of a rhombus bisect angles and are perpendicular to each other. We also see that diagonals of a rectangle are congruent. Through examples, we demonstrate how to find angle measures and lengths, applying theorems to determine if a given parallelogram is a rhombus, rectangle, or neither. Homework problems reinforce these concepts.

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Chapter 6: Quadrilaterals

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  1. Chapter 6: Quadrilaterals 6.4 Special Parallelograms

  2. Review

  3. Theorem 6-9 • Each diagonal of a rhombus bisects two angles of the rhombus.

  4. Theorem 6-10 • The diagonals of a rhombus are perpendicular.

  5. Example 1 • MNPQ is a rhombus. Find the measures of the numbered angles.

  6. Example 1a • Find the measures of the numbered angles in the rhombus.

  7. Theorem 6-11 • The diagonals of a rectangle are congruent.

  8. Example 2 • Find the length of FD in the rectangle if • FD = 2y + 4 and GE = 6y – 5.

  9. Theorem 6-12 • If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus. • (converse of Th. 6-9)

  10. Theorem 6-13 • If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. • (converse of 6-10)

  11. Theorem 6-14 • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. • (converse of Th. 6-11)

  12. Example 3 • Is the parallelogram a rhombus or a rectangle or neither?

  13. Example 3 • Is the parallelogram a rhombus or a rectangle or neither?

  14. Homework • P. 332 • 2-18 even, 22, 40, 44, 46, 50, 52

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