* Prove and apply properties of rhombuses and squares. * Use properties of rhombuses and squares to solve problems.

1. 2.7.3 Rhombi & Squares
The student is able to (I can):
• Prove and apply properties of rhombuses and squares.
• Use properties of rhombuses and squares to solve
problems.

2. rhombus A parallelogram with four congruent sides.
(Plural is either rhombi or rhombuses.)
If a parallelogram is a rhombus, then its
diagonals are perpendicular.

3. Proof:
Because BOWL is a rhombus,
Diagonals bisect each other, so
The reflexive property means that
Therefore, ∆OSB ≅ ∆OSW by SSS. This
means that ∠OSB ≅ ∠OSW. Since they
are also supplementary, they must be 90º.
B O
WL
S
≅BO OW.
≅BS WS.
≅OS OS.

4. If a parallelogram is a rhombus, then each
diagonal bisects a pair of opposite angles.
∠1 ≅ ∠2
∠3 ≅ ∠4
∠5 ≅ ∠6
∠7 ≅ ∠8
1 2 3
4
5
67
8
Since opposite angles are
also congruent:
∠1 ≅ ∠2 ≅ ∠5 ≅ ∠6
∠3 ≅ ∠4 ≅ ∠7 ≅ ∠8

5. Examples 1. What is the perimeter of a rhombus
whose side length is 7?
4(7) = 28
2. Find the value of x
The side = 10
Pyth. triple: 6, 8, 10
x = 6
3. Find the value of y
13y — 9 = 3y + 11
10y = 20
y = 2
x
8
Perimeter = 40
(3y+11)º
(13y—9)º
10

6. square A quadrilateral with four right angles and
four congruent sides.
Note: A square has all of the properties of
both a rectangle and a rhombus:
• Diagonals are congruent
• Diagonals are perpendicular
• Diagonals bisect opposite angles.