1. 6.4 Rhombuses, Rectangles, and Squares
Warm-Up Exercises
In parallelogram ABCD, m<A = 3x + 15 and
m<C = 5x – 17. What is the value of x?
2. Find the distance between K(1, 3) and M(3, 4).
3. In parallelogram KJLM, KJ = 10y – 5 and
LM = -6y What is the value of y?
4. The vertices of PQRS are P(-1, -3), Q(2, -4), R(5, -1), and S(2, 0). Is PQRS a parallelogram?

2. Parallelograms
Rectangles
Squares
Rhombuses

3. Rhombuses
Rectangles
Squares

4. Rhombuses Rhombus – a quadrilateral with four congruent sides
Demonstration of the Properties of Rhombuses
List of Properties of Rhombuses
Proving a Parallelogram is a Rhombus
List of Ways to Prove a Parallelogram is a Rhombus
Examples With Rhombuses
Main Page

5. Properties of Rhombuses
If a quadrilateral is a rhombus, then
it has four congruent sides.
its diagonals are perpendicular and bisect opposite angles.
Rhombus Main Page

6. Ways to Prove a Parallelogram is a Rhombus
A parallelogram is a rhombus if
1. it has four congruent sides.
2. its diagonals are perpendicular.
Rhombus Main Page

7. Rhombuses
In the diagram shown, PQRS is a rhombus. What is the value of y? P Q
2y + 3 S
5y - 6 R
Main Page

8. Rectangles Rectangle – a quadrilateral with four right angles
Demonstration of the Properties of Rectangles
List of Properties of Rectangles
Proving a Parallelogram is a Rectangle
List of Ways to Prove a Parallelogram is a Rectangle
Main Page

9. Properties of Rectangles
If a quadrilateral is a rectangle, then
it has four right angles.
its diagonals are congruent.
Rectangle Main Page

10. Ways to Prove a Parallelogram is a Rectangle
A parallelogram is a rectangle if
1. it has four right angles.
2. its diagonals are congruent.
Main Page

11. Squares
Square – a quadrilateral with four right angles and four congruent sides
Demonstration of the Properties of Squares
List of Properties of Squares
Proving a Parallelogram is a Square
List of Ways to Prove a Parallelogram is a Square
Main Page

12. Properties of Squares If a quadrilateral is a square, then
it has four right angles and four congruent sides.
its diagonals are congruent and perpendicular.
Square Main Page

13. Ways to Prove a Parallelogram is a Square
A parallelogram is a square if
1. it has four right angles and four congruent sides.
2. its diagonals are congruent and perpendicular.
Main Page