Rhombus and Square

1. Rhombus and Square

2. Goals • Define rhombus. Discuss properties. • Define square. Discuss properties. • Use properties to determine if a quadrilateral is a parallelogram, rectangle, rhombus, square.

3. Properties of a Parallelogram REVIEW !! • Definition: Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Characteristics of a Rectangle • See above • Definition: All four angles are congruent • Diagonals are congruent.

4. Rhombus - Definition The plural of rhombus is “rhombi” • A rhombus is a parallelogram where all 4 sides are congruent. The characteristics of parallelograms are also true for rhombus, since it is a special type of parallelogram.

5. Rhombus - Diagonals • The diagonals of a rhombus are perpendicular. A What is the relationship between AC and BD? D B C

6. Rhombus - Diagonals • If the diagonals of a parallelogram are perpendicular, then it is a rhombus. A If AC is perpendicular to BD and ABCD is a parallelogram, then ABCD is a rhombus D B C

7. Rhombus – Diagonals - Angles • The diagonals of a rhombus bisect the opposite angles. A D B C

8. Square - Definition • A square is a parallelogram where all 4 angles are congruent and all four sides are congruent. A square has all the same properties as a parallelogram, a rhombus, and a rectangle.

9. I’m thinking of a quadrilateral where all the sides are equal… what could it be? Rhombus or Square Parallelograms • Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Rectangles • All four angles are congruent • Diagonals are congruent. • ALL parallelogram properties. Rhombi • All four sides are congruent • Diagonals are perpendicular. • Opp. angles are bisected. • ALL parallelogram properties. Squares • The only regular quadrilateral. • ALL properties of para, rect, and rhom. I’m thinking of a quadrilateral where the opposite sides are parallel… what could it be? Para, Rect, Rhom, or Square

10. Parallelograms • Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Rectangles • All four angles are congruent • Diagonals are congruent. • ALL parallelogram properties. Rhombi • All four sides are congruent • Diagonals are perpendicular. • Opp. angles are bisected. • ALL parallelogram properties. Squares • The only regular quadrilateral. • ALL properties of para, rect, and rhom. Best Name??

11. Parallelograms • Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Rectangles • All four angles are congruent • Diagonals are congruent. • ALL parallelogram properties. Rhombi • All four sides are congruent • Diagonals are perpendicular. • Opp. angles are bisected. • ALL parallelogram properties. Squares • The only regular quadrilateral. • ALL properties of para, rect, and rhom. Best Name??

12. Parallelograms • Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Rectangles • All four angles are congruent • Diagonals are congruent. • ALL parallelogram properties. Rhombi • All four sides are congruent • Diagonals are perpendicular. • Opp. angles are bisected. • ALL parallelogram properties. Squares • The only regular quadrilateral. • ALL properties of para, rect, and rhom. Best Name??

13. Caution! There is a difference between… What could this be? What’s the best name? All we know FOR SURE is that it is a parallelogram. It COULD be a parallelogram or a rectangle.

14. Match the property with all of the types of quadrilateral which have that property. The diagonals are congruent. Parallelogram Rectangle Rhombus Square

15. Match the property with all of the types of quadrilateral which have that property. Both pairs of opposite sides are congruent. Parallelogram Rectangle Rhombus Square

16. Parallelograms • Both pairs opp. sides of are parallel. • Both pairs opp. sides are congruent • Both pairs opp. angles are congruent • All consecutive angles add to 180. • Diagonals bisect each other. • One pair of sides is parallel and congruent. Rectangles • All four angles are congruent • Diagonals are congruent. • ALL parallelogram properties. Rhombi • All four sides are congruent • Diagonals are perpendicular. • Opp. angles are bisected. • ALL parallelogram properties. Squares • The only regular quadrilateral. • ALL properties of para, rect, and rhom.

17. Quadrilaterals 4 sides, angles add to 360 Parallelograms Opp sides parallel, Opp sides congruent, Opp angles congruent, Consecutive angles =180, Diagonals bisect Rectangle All angles are congruent. Diagonals are congruent. Rhombus All sides are congruent. Diagonals are perpendicular. Opp angles are bisected. Square Everything