# Project 2: Geometry In Our World!

## Properties Of A Rectangle

What are some properties of a rectangle?

• Each interior angle is 90 degrees
• Opposite sides are parallel and of equal length
• All interior angles equal 360 degrees
• Opposite angles added together equal 180 degrees
Analysis

This window on this house is a rectangle. Each of the interior angles is a right angle (shown by the little house symbol in each corner of the window in red).

Also, the Opposite sides are equal. LINE AB and DC are parallel and they are opposite to each other. They both equal 1.05 units. The same things can be said about LINE AD and BC, and they both equal 0.65 units.

We know that the opposite lines are parallel because there is 4 C-patterns in total (Co-interior Angle theorem) and we know that 2 angles beside each other when added together, equal 180 degrees.

Finally, we know this is a rectangle because rectangles are quadrilaterals; the sum of their interior angles is 360 degrees. This rectangle's angles added together are 360 degrees and we know this by using our formula ((180 (n-2)) and multiplying 90 degrees by 4 for each of the angles which equals 360 degrees as well.

## Properties Of A Triangle

What are some properties of a triangle?

• A triangle has three sides and three angles
• The three angles always add to 180 degrees

Analysis

This triangle shown in the picture is a scalene triangle. We know this because the 3 angles in the triangle are not all equal. The 3 interior angles add up to 180 degrees. We know this because of the formula '180 (n-2)'. To check if this formula is correct, we are going to calculate the sum of the the 3 interior angles; ∠ABC, ∠ACB, ∠CAB.

(57.32 + 59.34 + 63.35 = 180.01)

This shows that this shape is an triangle.

## Properties Of A Parallelogram

What are some properties of a Parallelogram?

• Opposite sides are parallel
• Opposite sides are equal in length
• All interiors equal to 360 degrees
• Opposite angles added together equal 180 degrees
Analysis

The quadrilateral in this picture is a parallelogram. We know this because the sides opposite to each other are parallel.These lines are parallel because they are equal of length and they follow the Co-Interior Angle Theorem (C-Pattern) in which they are 2 pairs of C patterns (4 in total) in the whole parallelogram.

The following lines create the C Pattern:

1. LINE CF, CD and ED ( ∠DCF ∠EDC)

2. LINE CD, DE, and EF ( ∠EDC ∠FED)

3. LINE DE, EF, and CF ( ∠FED ∠CFE)

4. LINE DC, CF, and FE ( ∠DCF ∠CFE)

The opposite sides in the parallelogram are clearly equal; (LINES CF & DE both equal 1.08 units)/ (LINES DC & EF both equal 2.88 units)

The opposite angles also equal the same. (∠FED and ∠DCF both are 95.57 degrees, ∠EDC and ∠CFE are both 84.43 degrees.)

We know this 4 sided shape is a parallelogram because of the sum of the interior angles (∠FED,∠DCF,∠EDC and ∠CFE) which equal to 360 degrees ((180 (4-2)).

(95.57 (2) + 84.43 (2) = 360)

## Properties Of A Pentagon

What are some properties of a Pentagon?

• 5 sides
• Interior angles equal to 540 degrees

Analysis

We know this is a Pentagon because the shape clearly has 5 sides.

We also know this shape is a pentagon because the sum of the interior angles adds up to 540 degrees. (73.16 + 140.81 + 88.98 + 90.99 + 146.27 = 540 degrees)

We know the sum of the interior angles of a pentagon is 540 degrees because of the following equation;

(180 (n-2))

= (180 (5-2))

= (180 (3))

= 540

## Properties Of A Square

What are some properties of a Square?

• all sides are equal in length
• Each interior angle is 90 degrees
• Opposite sides are parallel
Analysis

We know this quadrilateral is a square because all sides equal 2 units in length.

The square has 4 angels and the sum of the interior angles is 360 degrees, we know this because all 4 angles are 90 degrees. (90x4=360)

We know the sum of the interior angles of this shape equal 360 because of the formula for interior angles; 180 (n-2)

In this shape all opposite sides are parallel.

We know this because, this shape has 4 C-patterns (Co-Interior Angle Theorem) which proves that all angles opposite to each other are equal and 2 angles beside each other added together equal 180 degrees.

## Properties Of A Hexagon

What are some properties of a Hexagon?

• 6 sides
• All interior angles equal to 720 degrees
Analysis

We know that the shape above is a hexagon because there are 6 sides shown in the picture.

We also know that the shape is a hexagon because the sum of the interior angles adds up to 720 degrees. (117.34 + 119.17 + 130.03 + 120.14 + 116.77 + 116.56 = 720 degrees)

180(n-2))
=180(6-2))
=180(4))
=720

## Sources Used

• Geogebra
• MathIsFun.com/Geometry
• Smore
• CoolMath.com