jose martinez-quad project

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PARALLELOGRAM STORY

ByJose Martinez

IntroductionMy 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.

My Parallelogram

● Opposite sides are congruent.● Opposite angles are congruent.● Consecutive angles are

supplementary.● Opposite sides are parallel.

● Diagonals bisect each other.

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

ComparisonSquare and a rectangle

Square and a rhombus

● Both shapes contain 90 angles.● Both shapes contain congruent diagonals.● Both shapes contain 2 pairs of

congruent sides.● Both shapes contain 2 pairs

of parallel sides.

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Trapezoids and a square ● Both shapes contain at least one pair of parallel sides.● Both shapes contain at least one pair of congruent sides.

● Both shapes contain bisecting diagonals.● Both shapes contain two pairsof parallel sides.● Both shapes contain 4

congruent sides.

ContrastSquare and rectangle● A square containsfour congruent sides while a rectangle doesn’t.● A square has bisectingdiagonals.

Square and Rhombus● A square contains congruent diagonals.● A square containsfour right angles.

Square and Trapezoid● A square has two pairsof parallel sides● A square has four congruent sides.● A square has 4 right angles.

BIG Picture

QUADRILATERAL

PARALLELOGRAM

RectangleRhombus

Square

○ Has four right angles○ Has two pairs of

congruent sides.○ Has two pairs of parallel

sides.○ Has congruent diagonals.○ 4 right angles.

● Has bisecting diagonals.

● Has 4 congruent sides.

● Has two pairs of parallel sides.

● Has opposite congruent angles.

ProblemA(1,7)

B(6,5)

C(4,0)

D (-1,2)

Prove that quadrilateral ABCD is a square.

SolveA

B

C

D

You can tell that this "triangle" has gone up 5 and gone 2 right.

To solve this you must first... Prove that all sides are congruent

Knowing this you know that when you use the Pythagoreantheorem which is a2 + b2 = c2 will equal the length of the side.2^2+5^2=c^24+25=c^2√29=√c^2Rounded 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.

SolveA

B

C

D

Then you must ... Prove that all angles are right angles.To do this you must prove that the consecutive sides have negative reciprocal slopes.

You can tell that this "triangle" has gone up 5 and gone 2 right.

M<AB=-2/5M<DA=5/2M<DC=-2/5M<CB=5/2

ExampleA 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.

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.