Properties of Rhombuses, Rectangles, and Squares

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Presentation transcript:

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares A rhombus is a parallelogram with four congruent sides.

Properties of Rhombuses, Rectangles, and Squares A rectangle is a parallelogram with four right angles.

Properties of Rhombuses, Rectangles, and Squares A square is a parallelogram with four congruent sides and four right angles.

Section 6.4 – Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares Problem 1: Is Parallelogram ABCD a rhombus, rectangle or square? Explain!

Properties of Rhombuses, Rectangles, and Squares Problem 1b: Is Parallelogram EFGH a rhombus, rectangle or square? Explain!

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares Problem 2: What are the measures of the numbered angles in rhombus ABCD?

Properties of Rhombuses, Rectangles, and Squares Problem 2: What are the measures of the numbered angles in rhombus PQRS?

Properties of Rhombuses, Rectangles, and Squares Problem 2: What are the measures of the numbered angles in the rhombus?

Properties of Rhombuses, Rectangles, and Squares Problem 2: What are the measures of the numbered angles in the rhombus?

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares Problem 3: In rectangle RSBF, SF = 2x + 15 and RB = 5x – 12. What is the length of a diagonal?

Properties of Rhombuses, Rectangles, and Squares Problem 4: LMNP is a rectangle. Find the value of x and the length of each diagonal LN = 5x – 8 and MP = 2x + 1

Properties of Rhombuses, Rectangles, and Squares Problem 5: Determine the most precise name for each quadrilateral.

Properties of Rhombuses, Rectangles, and Squares Problem 6: List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square. Opposite angles are congruent.

Properties of Rhombuses, Rectangles, and Squares Problem 6b: List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square. Diagonals are congruent

Properties of Rhombuses, Rectangles, and Squares Problem 6c: List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square. Each diagonal bisects opposite angles

Properties of Rhombuses, Rectangles, and Squares Problem 6d: List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square. Opposite sides are parallel

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares Problem 1: Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

Conditions for Rhombuses, Rectangles, and Squares Problem 1b: Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

Conditions for Rhombuses, Rectangles, and Squares Problem 1c: Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

Conditions for Rhombuses, Rectangles, and Squares Problem 1d: Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

Conditions for Rhombuses, Rectangles, and Squares Problem 2: For what value of x is parallelogram ABCD a rhombus?

Conditions for Rhombuses, Rectangles, and Squares Problem 2b: For what value of x is the parallelogram a rectangle?

Conditions for Rhombuses, Rectangles, and Squares Problem 2c: For what value of x is the parallelogram a rhombus?

Conditions for Rhombuses, Rectangles, and Squares Problem 2d: For what value of x is the parallelogram a rectangle?

Conditions for Rhombuses, Rectangles, and Squares Problem 2e: For what value of x is the parallelogram a rectangle?

Conditions for Rhombuses, Rectangles, and Squares Problem 3: Builders use properties of diagonals to “square up” rectangular shapes like building frames and playing-field boundaries. Suppose you are on the volunteer building team at the right. You are helping to lay out a rectangular patio for a youth center. How can you use the properties of diagonals to locate the four corners?

Conditions for Rhombuses, Rectangles, and Squares Problem 4: Determine whether the quadrilateral can be a parallelogram. Explain! The diagonals are congruent, but the quadrilateral has no right angles.

Conditions for Rhombuses, Rectangles, and Squares Problem 4b: Determine whether the quadrilateral can be a parallelogram. Explain! Each diagonal is 3 cm long and two opposite sides are 2 cm long.

Conditions for Rhombuses, Rectangles, and Squares Problem 4c: Determine whether the quadrilateral can be a parallelogram. Explain! Two opposite angles are right angles but the quadrilateral is not a rectangle.

Conditions for Rhombuses, Rectangles, and Squares

Conditions for Rhombuses, Rectangles, and Squares