1. Properties of Rhombuses, Rectangles, and Squares

2. What is a rhombus?
A rhombus is a parallelogram that has four congruent sides.
That means that the opposite sides must also be parallel.
The diagonals of a rhombus form perpendicular lines.

3. Rhombus cont…
The diagonals bisect the interior angles.

4. Rectangles A rectangle is a parallelogram with 4 right angles.
Therefore, opposite sides must also be parallel.
The diagonals of a rectangle are congruent.

5. Squares
A square is a parallelogram with 4 right angles AND 4 congruent sides.
Because a parallelogram has parallel opposite sides, a square has parallel opposite sides.

6. Trapezoids
A trapezoid is a quadrilateral with 1 pair of parallel sides.

7. Can it be…? Can any square be a rectangle? Yes!
Can any rectangle be a square?
No!
Can any square be a rhombus?
Can any rectangle be a rhombus?

8. m<A = m<C ALWAYS m<B = m<C Sometimes m<B = m<D
Suppose you have a rhombus ABCD… When are the following true? Sometimes, never, or always A B C D
m<A = m<C
ALWAYS
m<B = m<C
Sometimes
m<B = m<D
ALWAYS
AB = BC
ALWAYS
AB = DC
ALWAYS

9. M<A = m<C ALWAYS m<B = m<C ALWAYS m<B = m<D ALWAYS
Suppose you have a rectangle ABCD… when are the following true? Always? Never? Sometimes? A B C D
M<A = m<C
ALWAYS
m<B = m<C
ALWAYS
m<B = m<D
ALWAYS
Sometimes
AB = BC
AB = DC
ALWAYS

10. One of these is not a rhombus… which one is not a rhombus?

11. First classify the quadrilateral then find x and y
Rhombus
5x + 6 = 8x
6 = 3x
2 = x
< Q and < P should be supplementary!
12y – = 180
12y + 96 = 180
12y = 84
y = 7

12. First classify the quadrilateral then find x and y
Square
2x + 1 = 4x - 7
2x + 8 = 4x
8 = 2x
4 = x
< KLN and < NLM should be complementary!
7y = 90
7y + 48 = 90
7y = 42
y = 6

13. Given that WXYZ is a rhombus…what do we know about the figure?
The diagonals bisect the interior angles.
A rhombus is a parallelogram that has four congruent sides.
That means that the opposite sides must also be parallel.
The diagonals of a rhombus form perpendicular lines.
12.5
34º
56º
56º
34º
12.5
12.5
10.4
34º
56º
56º Z Y
12.5
Cos(56) = 7/x
7/Cos(56) = x
12.5 = x
SOH CAH TOA!

14. The figure below is a rectangle Find the missing angles and sides
m<TPQ
m<PST
m<PTQ PS PR
HINT: PTQ is what kind of triangle?