1. Rhombuses, Rectangles, and Squares

2. Parallelograms
Rhombus is a parallelogram with four congruent sides.

3. Rhombus The diagonals of a rhombus are PERPENDICULAR
All 4 sides are congruent
Opposite angles are congruent
Consecutive angles (same-side interior) are supplementary
Diagonals Bisect each other
The diagonals of a rhombus are PERPENDICULAR

4. mMTL = 90o 90 + 50 + x = 180 140 + x = 180 x = 180 - 140 x = 40o
Diagonals of rhombus are perpendicular
x = 180
triangle sum theorem
140 + x = 180
x =
x = 40o

5. Area of a Rhombus
Area = Diagonal x Diagonal 2
A = d1•d2

6. A = d1d2 2
A = d1d2 2
= (4)(6) 2
= (5 + 5)(4 + 4) 2
= (10)(8) 2
= (24)/2
= 12 mm2
= 40 cm2

7. Parallelograms
Rectangles is a parallelogram with four right angles.

8. Properties of Rectangle
Opposite sides are congruent
All angles are 90°
Diagonals are Congruent
Diagonals Bisect
AD BC

9. AD = 10 and CB = x. Find the value of x.
Ex. 4 ABCD is a rectangle.
AD = 10 and CB = x. Find the value of x.
x = 10 units
Diagonals of rectangle are congruent

10. 4x + 10 = 5x – 20 4 x – 5x = - 20 – 10 - x = - 30 x = 30 ZT = RZ
diagonals bisect each other in rectangle
ZT = 2x + 5
2(2x + 5) = 5x - 20
diagonals are congruent in rectangle
4x + 10 = 5x – 20
4 x – 5x = - 20 – 10
- x = - 30
x = 30

11. Parallelograms
Squares is a parallelogram with four congruent sides and four right angles.

12. All sides are congruent All angles are 90° Diagonals Bisect
Properties of a Square
All sides are congruent
All angles are 90°
Diagonals Bisect
Diagonals are Congruent
Diagonals are Perpendicular

13. Ex. 1) In the diagram RSTU is a square.
a) Find UT, RU, and RS.
b) Find mR, mS, mT, and mU
Square has 4 congruent sides
UT  RU  RS = 7 units
Square has 4 congruent angles
mR  mS  mT  mU = 90o