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 GEOMETRY: Chapter 6 6.4: Properties of Rhombuses, Rectangles, and Squares

Rhombus Corollary A quadrilateral is a rhombus if and only if it has four congruent sides. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 533.

Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 533.

Square Corollary A quadrilateral is a square if and only if it is a rhombus and a rectangle. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 533.

Ex.1: For any rectangle ABCD, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning.

Ex.1: For any rectangle ABCD, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. ANSWERS: always. All rectangles are parallelograms, and opposite sides of parallelogram are congruent. Sometimes; AB is congruent to BC provided the rectangle ABCD is a square. But not all rectangles are squares.

Classify the special quadrilateral. Explain your reasoning. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 534.

Classify the special quadrilateral. Explain your reasoning. Answer: rhombus; it is a parallelogram because opposite angles are congruent. Since a pair of adjacent sides are congruent, all four sides are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 534.

Theorem 6.11 A parallelogram is a rhombus if and only if its diagonals are perpendicular. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 535.

Theorem 6.12:A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 535.

Theorem 6.13 A parallelogram is a rectangle if and only if its diagonals are congruent. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 535.

Ex. 3: Sketch a square EFGH. List everything that you know about it.

Ex. 3: Sketch a square EFGH. List everything that you know about it.

Ex. 4: You are building a case with glass shelves for collectibles. Given the shelf measurements in the diagram, can you assume that the shelf is a square? Explain. You measure the diagonals; they are both 33.94 inches. What can you conclude about the shape? Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 536.

Ex. 4: You are building a case with glass shelves for collectibles. Given the shelf measurements in the diagram, can you assume that the shelf is a square? Explain. You measure the diagonals; they are both 33.94 inches. What can you conclude about the shape? Answer: a) No. It has four congruent sides so it is a rhombus. However, we do not know whether the angles are right angles. b) It is a square. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 536.

6.4, p. 351, #3-21 all, 33-38 all