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# Geom 6point4 97

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### Geom 6point4 97

1. 1. 6.4 Rhombuses, Rectangles, & Squares <ul><li>Objective: </li></ul><ul><li>Use properties of sides and angles and diagonals of rhombuses, rectangles, and squares </li></ul>
2. 2. Rhombus <ul><li>A rhombus is a parallelogram with 4 congruent sides. </li></ul>
3. 3. Rectangle <ul><li>A rectangle is a parallelogram with 4 right angles </li></ul>
4. 4. Square <ul><li>A square is a parallelogram with 4 congruent sides and 4 right angles </li></ul>
5. 5. Always, sometimes, or never? <ul><li>A rhombus is a rectangle </li></ul><ul><li>sometimes </li></ul><ul><li>A parallelogram is a rectangle </li></ul><ul><li>sometimes </li></ul><ul><li>A square is a rectangle </li></ul><ul><li>always </li></ul>
6. 6. Always, sometimes, or never? <ul><li>A square is a rhombus </li></ul><ul><li>always </li></ul><ul><li>A rhombus is a square </li></ul><ul><li>sometimes </li></ul><ul><li>A rectangle is a rhombus </li></ul><ul><li>sometimes </li></ul>
7. 7. If you know ABCD is a rectangle, what else do you know? <ul><li>Opposite sides are </li></ul><ul><li>|| and  </li></ul><ul><li>Opposite angles are </li></ul><ul><li> </li></ul><ul><li>Consecutive angles are </li></ul><ul><li>supplementary </li></ul><ul><li>Diagonals </li></ul><ul><li>bisect each other </li></ul>A B C D
8. 8. Corollaries About Special Parallelograms <ul><li>Rhombus Corollary </li></ul><ul><li>A quadrilateral is a rhombus if and only if it has 4 congruent sides </li></ul><ul><li>Rectangle Corollary </li></ul><ul><li>A quadrilateral is a rectangle if and only if it has 4 right angles </li></ul><ul><li>Square Corollary </li></ul><ul><li>A quadrilateral is a square if and only if it is a rhombus and a rectangle </li></ul>
9. 9. Using Diagonals of Special Parallelograms <ul><li>3 theorems . . . </li></ul>
10. 10. Theorem <ul><li>A parallelogram is a rhombus if and only if its diagonals are perpendicular </li></ul>
11. 11. Theorem <ul><li>A parallelogram is a rhombus if and only each diagonal bisects a pair of opposite angles </li></ul>
12. 12. Theorem <ul><li>A parallelogram is a rectangle if and only if its diagonals are congruent. </li></ul>
13. 13. Do p. 351 1-21 <ul><li>Homework: Do worksheets. </li></ul>