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Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares

Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares. Goal: You will use properties of rhombuses, rectangles, and squares. Special Types of Parallelograms A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles.

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Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares

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  1. Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares Goal: You will use properties of rhombuses, rectangles, and squares.

  2. Special Types of 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.

  3. Proving that a Quadrilateral is a Rhombus, Rectangle, or Square • Rhombus Corollary: A quadrilateral is a rhombus if and only if it has four congruent sides. • Rectangle Corollary: A quadrilateral is a rectangle if and only if it has four right angles.

  4. Square Corollary: A quadrilateral is a square if and only if it is a rhombus and a rectangle. Relationships Among Parallelograms, Rhombuses, Rectangles, and Squares

  5. Ex.1: For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. a. b. Ex.2: Classify the special quadrilateral. Explain your reasoning.

  6. Diagonals • Theorem 8.11: A parallelogram is a rhombus if and only if its diagonals are perpendicular. • Theorem 8.12: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. • Theorem 8.13: A parallelogram is a rectangle if and only if its diagonals are congruent.

  7. Ex.3: Suppose the diagonals of a parallelogram are both perpendicular and congruent. What type of special quadrilateral is it? Explain. Ex.4: Sketch rectangle ABCD. List everything that you know about it. Ex.5: Sketch square PQRS. List everything that you know about it. Ex.6: Sketch rhombus GHIJ. List everything that you know about it.

  8. Ex.7: You are building a frame for a window. The window will be installed in the opening shown in the diagram. • The opening must be a rectangle. Given the measurements in the diagram, can you assume that it is? Explain. • You measure the diagonals of the opening. The diagonals are 54.8 inches and 55.3 inches. What can you conclude about the shape of the opening?

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