6-4 Properties of Rhombuses, Rectangles, and Squares

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6.4 Rhombuses, Rectangles, and Squares

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Presentation transcript:

6-4 Properties of Rhombuses, Rectangles, and Squares

Special Parallelograms A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles.

Classifying Special Parallelograms Is parallelogram ABCD a rhombus, a rectangle, or a square? Explain. Is parallelogram EFGH a rhombus, a rectangle, or a square? Explain.

Rhombus Properties Theorem 6-13: If a parallelogram is a rhombus, then its diagonals are perpendicular. Theorem 6-14: If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Finding Angle Measures What are the measures of the numbered angles in rhombus ABCD?

 What are the measures of the numbered angles in rhombus PQRS?

Rectangle Properties Theorem 6-15: If a parallelogram is a rectangle, then its diagonals are congruent.

Finding Diagonal Length If SF = 2x + 15 and RB = 5x – 12, what is the length of a diagonal of rectangle RSFB?

 If LN = 4x – 17 and MO = 2x + 13, what are the lengths of the diagonals of rectangle LMNO?