6 5 Rhombi and Squares Rhombus o Quad

6. 5 Rhombi and Squares

Rhombus o Quad with 4 sides

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

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

Quadrilaterals Parallelograms Rhombi Squares Rectangles

Example o o o 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 o Rhombus Properties n n n n 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 o Square Properties n n n n n 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 o p. 352 11, 15 -18, 19 -25 odd, 31 -34