6-4 Properties of Rhombuses, Rectangles, and Squares

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Presentation transcript:

6-4 Properties of Rhombuses, Rectangles, and Squares

Rectangles Definition: A quadrilateral with four right angles. (this is all we know) What condition does this satisfy to be classified a parallelogram?

Properties of a Rectangle -Opposite sides are congruent -Opposite sides are parallel -Opposite angles are congruent -Diagonals bisect each other -Consecutive angles supplementary -Interior angles sum to 360 Why are these 6 properties true for a rectangle? -The diagonals of a rectangle are congruent. Theorem

Label everything we know about this figure.

Rhombus Definition: A quadrilateral with four congruent sides. (all we know) What allows us to classify this as a parallelogram?

Properties of a Rhombus -Opposite sides are congruent -Opposite sides are parallel -Opposite angles are congruent -Diagonals bisect each other -Consecutive angles supplementary -Interior angles sum to 360 Why are these 6 properties true for a rhombus? The diagonals of a rhombus are perpendicular. Each diagonal of a rhombus bisects 2 angles of the rhombus Theorem Theorem

Label everything we know about this figure.

Square Definition: A quadrilateral with four right angles and four congruent sides.

Properties of a square -Opposite sides are congruent -Opposite sides are parallel -Opposite angles are congruent -Diagonals bisect each other -Consecutive angles supplementary -Interior angles sum to 360 Is a square a rectangle? Why or why not? Is a square a rhombus? Why or why not? Do we then know that a square also shares the properties of those 2 figures?

Label everything that we know about this square

(If I were to place the first figure in front of you, would it also be the second figure) Is a rectangle a square? Is a rhombus a square?

Theorem If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle. (what would we need to know for it to be a square) If 2 consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. Theorem

Quadrilateral Flow Chart Polygons Quadrilateral Parallelogram Kite Square Rectangle Rhombus Trapezoid