6.5 Rhombi and Squares.

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Presentation transcript:

6.5 Rhombi and Squares

Rhombus Quad with 4  sides

Rhombus Theorem 6.15: The diagonals of a rhombus are  . Theorem 6.16: If the diagonals of a parallelogram are , then the parallelogram is a rhombus. Theorem 6.17: Each diagonal of a rhombus bisects a pair of opposite angles. All 4 of the s are .

Example Refer to Example #2 picture on page 349 Do Check Your Progress #2 Answer: 114

Square Both a rhombus and a rectangle All sides are  All angles are right angles (90°)

Quadrilaterals Parallelograms Rectangles Rhombi Squares

Example Given the vertices J(5,0), K(8, -11), L (-3,-14), M(-6,-3), determine whether parallelogram JKLM is a rhombus, a rectangle, or a square. List all that apply. Use the distance formula to compare the lengths of the diagonals. Use the slope formula to determine if the sides are perpendicular. Answer: Square, rectangle, and rhombus, all sides are congruent and perpendicular.

Summaries Rhombus Properties Square Properties Opposites sides are  Opposite angles are  Consecutive angles are supplementary. Diagonals bisect each other Diagonals are perpendicular Each diagonal bisects two angles. 4 sides are  Square Properties Opposites sides are  Opposite angles are  Consecutive angles are supplementary. Diagonals bisect each other Diagonals are perpendicular Each diagonal bisects two angles. All four angles are right angles. Diagonals are  4 sides are 

Homework #41 p. 352 11, 15-18, 19-25 odd, 31-34