6-5 Study Guide and Intervention Rhombi and Squares Properties of Rhombi and Squares A rhombus is a quadrilateral with four congruent sides. Opposite sides are congruent, so a rhombus is also a parallelogram and has all of the properties of a parallelogram. Rhombi also have the following properties. The diagonals are perpendicular. bisects and Each diagonal bisects a pair of opposite angles. bisects and A square is a parallelogram with four congruent sides and four congruent angles. A square is both a rectangle and a rhombus; therefore, all properties of parallelograms, rectangles, and rhombi apply to squares. Example: In rhombus = 32. Find the measure of each numbered angle. ABCD, is a rhombus, so the diagonals are perpendicular and is a right triangle. ABCD △ABE Thus = 90 and = 90 32 or 58. The diagonals in a rhombus bisect the vertex – angles, so = Thus, = 58. A rhombus is a parallelogram, so the opposite sides are parallel. and are alternate interior angles for parallel lines, so = 32. Exercises Quadrilateral is a rhombus. Find each value or measure. ABCD 1. If = 60, find 2. If = 8, find AE AC. 3. If = 26 and = 20, find 4. Find AB BD AE. 5. If = 58, find 6. If = 3x 1 and = 16, find AE AC x. – 7. If = 6y and = 2y + 10, find y. 8. If = 2x + 4 and = 4x 4, find AD CD x. –
6-5 Study Guide and Intervention Rhombi and Squares Properties of Rhombi and Squares A rhombus is a quadrilateral with four congruent sides. Opposite sides are congruent, so a rhombus is also a parallelogram and has all of the properties of a parallelogram. Rhombi also have the following properties. The diagonals are perpendicular. Each diagonal bisects a pair of opposite angles. bisects and bisects and A square is a parallelogram with four congruent sides and four congruent angles. A square is both a rectangle and a rhombus; therefore, all properties of parallelograms, rectangles, and rhombi apply to squares. Example: In rhombus ABCD, = 32. Find the measure of each numbered angle. ABCD is a rhombus, so the diagonals are perpendicular and △ABE is a right triangle. Thus = 90 and = 90 – 32 or 58. The diagonals in a rhombus bisect the vertex angles, so = Thus, = 58. A rhombus is a parallelogram, so the opposite sides are parallel. and are alternate interior angles for parallel lines, so = 32. Exercises Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If = 60, find 2. If AE = 8, find AC. 3. If AB = 26 and BD = 20, find AE. 4. Find 5. If = 58, find 6. If AE = 3x – 1 and AC = 16, find x. 7. If = 6y and = 2y + 10, find y. 8. If AD = 2x + 4 and CD = 4x – 4, find x.
Rhombi_and_Squares.docx