1. PARALLELOGRAM
STORY
{ By
Jose Martinez

2. Introduction
My name is Jose Martinez and
this is my parallelogram story
project. I am at this time taking
a geometry class taught by Ms.
Bush. The goal of this project is
simple. My goal is to tell you a
story , a parallelogram story.

3. My Parallelogram
● Opposite sides are congruent.
● Opposite angles are congruent.
● Consecutive angles are
supplementary.
● Opposite sides are parallel.

4. ● Diagonals bisect each
other.
● Diagonals are congruent.
● 2 pairs of parallel lines.
● 4 congruent sides.

5. Comparison
Square and a Square and a
rectangle rhombus
● Both shapes contain 90o ● Both shapes contain bisecting
angles. diagonals.
● Both shapes contain congruent ● Both shapes contain two pairs
diagonals. of parallel sides.
● Both shapes contain 2 pairs of ● Both shapes contain 4
congruent sides. congruent sides.
● Both shapes contain 2 pairs
of parallel sides.
Trapezoids and a square
● Both shapes contain at least one pair of parallel sides.
● Both shapes contain at least one pair of congruent sides.

6. Contrast
Square and
rectangle Square and
● A square contains Rhombus
four congruent sides ● A square contains
while a rectangle doesn’t. congruent diagonals.
● A square has bisecting ● A square contains
diagonals. four right angles.
Square and
Trapezoid
● A square has two pairs
of parallel sides
● A square has four
congruent sides.
● A square has 4 right
angles.

7. BIG Picture
R AL
A TE
L PARALLELOGRAM
D RI
Q UA Rhombus Rectangle
○ Has four right angles
● Has bisecting ● Has two pairs ○ Has two pairs of
diagonals. of parallel congruent sides.
● Has 4 congruent sides. sides. ○ Has two pairs of parallel
● Has opposite sides.
congruent ○ Has congruent diagonals.
angles. ○ 4 right angles.
Square

8. Problem
A
(1,7)
Prove that
quadrilateral B
(6,5)
ABCD is a
square. D
(-1,2)
C
(4,0)

9. Solve
You can tell that this
"triangle" has gone up 5 and
gone 2 right.
To solve this you A
must first...
Prove that all
sides are B
congruent
D
C
Knowing this you know that when you use the Pythagorean
theorem which is a2 + b2 = c2 will equal the length of the
side.
2^2+5^2=c^2
4+25=c^2
√29=√c^2
Rounded answer is 5.4 units, this is the hypotenuse or side.
The process is then repeated for all four sides with same results.
This makes all sides congruent.

10. Solve
Then you must ... You can tell that this "triangle" has gone
up 5 and gone 2 right.
Prove that all angles are A
right angles.To do this
you must prove that the
consecutive sides have
negative reciprocal B
slopes.
D
C
M<AB=-2/5
M<DA=5/2
M<DC=-2/5
M<CB=5/2

11. Example
A real life example of my shape can be seen anywhere ,
whether it’s a problem of area or other things squares are
very simple but at the same time complex shapes.
Squares can appear on the street ,at stores and even at
home.

12. In this project I experienced countless situations in
which I never thought squares would appear in.
What was most interesting in this whole project is
that although squares seem simple the math and
logical reasoning behind them is great in numbers
and ways. I liked the idea behind photo story and
enjoyed the format in which it was used. I would
have wanted it to be able to use it with other
shapes as a manner of opening up the ways and
components of shapes.