1. 6.4: Properties of Rhombuses, Rectangles, and Squares
GEOMETRY: Chapter 6
6.4: Properties of Rhombuses, Rectangles, and Squares

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

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

4. 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, P. 533.

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

6. 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.

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

8. 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, P. 534.

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

10. 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, P. 535.

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

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

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

14. 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 inches. What can you conclude about the shape?
Image taken from: Geometry. McDougal Littell: Boston, P. 536.

15. 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 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, P. 536.

16. 6.4, p. 351, #3-21 all, all