1. Date: Topic: Rhombi, Rectangles, and Squares (7.2)
Warm-up: A B
2x + 5
Find x.
2x + 5
2x x + 5 = 50
4x + 10 = 50 C D
-10
-10
4x = 40 4 4
x = 10

2. Rhombus
10 cm
A rhombus is a quadrilateral with two sets of parallel sides and all four congruent sides.
10 cm
10 cm
10 cm
Since a rhombus is a special parallelogram, it has all the properties of a parallelogram :
- Opposite angles are congruent.
- Opposite sides are congruent.
- The diagonals bisect each other.

3. Properties of a Rhombus
A Rhombus also has its own unique properties:
The diagonals bisect the angles.
The diagonals are perpendicular bisectors of each other.
Because of this, the diagonals of a rhombus create four congruent right triangles.

4. Rectangle A rectangle is a parallelogram with four 90 degree angles.
20 cm
5 cm
5 cm
20 cm
Since a rectangle is a special parallelogram, it has all the properties of a parallelogram :
- Opposite angles are congruent.
- Opposite sides are congruent.
- The diagonals bisect each other.

5. Properties of a RectangleB D C
Rectangles also have their own unique properties:
- The diagonals of a rectangle are congruent.
- The diagonal bisections are congruent.

6. Square A B
A square is a rhombus (4 congruent sides and 2 sets of parallel sides) with four 90 degree angles (like a rectangle).
A square is a special type of rectangle, so it also has congruent diagonals. D C
Since a square is also a special kind of rhombus, it has all the properties of a rhombus and some of unique ones:
- Diagonals bisect the angles (all are congruent).
- Diagonals are perpendicular bisectors of each other (all
bisected segments are congruent).
- Diagonals form four congruent isosceles right triangles.

7. The diagonals of a rhombus are perpendicular bisectors of each other.
Find the missing angle measurements.
This shape is a rhombus. 5 4
90° 1
The diagonals of a rhombus are perpendicular bisectors of each other. 2
90° 3
35°
35°
The diagonals of a rhombus are angle bisectors.

8. -125° -125° The angles of a triangle add up to 180 degrees. 5 4 55°
90°
55°
-125°
-125°
90°
35°
35°
The diagonals of a rhombus are angle bisectors.