Rhombi and Squares Rhombus - A parallelogram with four congruent sides. Theorem 8.15 The diagonals of a rhombus are perpendicular. Theorem 8.17 Each diagonal of a rhombus bisects a pair of opposite angles. Theorem 8.16 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Rhombi and Squares Summary of Properties of a Rhombus A rhombus has all the properties of a parallelogram. All sides are congruent. Diagonals are perpendicular. Diagonals bisect the angles of the rhombus.

Use rhombus ABCD and the given information to find the value of each variable. Answer: 8 or –8 Answer: Example 5-2e

Rhombi and Squares Square - A parallelogram with both four equal sides and four equal angles. A square is a rectangle and a rhombus. Summary of Properties of a Square A square has all the properties of a parallelogram. A square has all the properties of a rectangle. A square has all the properties of a rhombus.

Kayla has a garden whose length and width are each 25 feet Kayla has a garden whose length and width are each 25 feet. If she places a fountain exactly in the center of the garden, how far is the center of the fountain from one of the corners of the garden? Answer: about 17.7 feet Example 5-4d

Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain. Example 5-3a

Plan If the diagonals are perpendicular, then ABCD is either a rhombus or a square. The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square. Solve Use the Distance Formula to compare the lengths of the diagonals. Example 5-3a

Use slope to determine whether the diagonals are perpendicular. Since the slope of is the negative reciprocal of the slope of the diagonals are perpendicular. The lengths of and are the same so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square. Example 5-3b