# Geometry In Our World

### Project 2 // By: Ife & Nathaniel

## Theorem #1When constructing this building, the corporation responsible used ‘ | ## Theorem #2
| ## Theorem #3This building seems to be made out of triangles, which are arranged in ways that they make many rhombus-like polygons. These 4-sided polygons must follow the theorem of CFE = 105.1°, FED = 67.3°, EDC = 104.2°, DCF = 83.4° The sum of these angles is 360° |

## Theorem #1

When constructing this building, the corporation responsible used ‘**Isosceles Triangle Theorem’**. I know this because the theorem states that If two sides of a triangle are congruent, the angles opposite them are congruent, making it an isosceles triangle. Sides A&C have the same side length, this means that angle CDE and CED have the same angle measure, therefore this triangle is an isosceles triangle.

## Theorem #2

*Sum of the Interior Angles of a Triangle:* This Theorem states that if you were to find all three of the interior angles of a triangle, then calculate the sum of the angles, it will always equal 180°. We have successfully calculated all of interior angles of this triangle. CDE = 48.6°, DEC = 48.6°, ECD = 82.8°

## Theorem #3

This building seems to be made out of triangles, which are arranged in ways that they make many rhombus-like polygons. These 4-sided polygons must follow the theorem of **‘Sum of the Interior Angles of a Polygon’. This **theorem sates the interior angles of any quadrilateral must equal 360°.

CFE = 105.1°, FED = 67.3°, EDC = 104.2°, DCF = 83.4°

The sum of these angles is 360°

## Theorem #4Opposite G&B = 86.5° each A&E = 93.5° each | ## Theorem #5Midpoints of a Triangle: Triangle FDC is made up of 4 smaller triangles. The area of triangle FDC IS 17.6 cm2. The midpoints of this triangle spilt the triangle into four. The total are of triangle FDC is 17.6cm2, so the area of FEG, which is 1/4th must be 4.4cm2. | ## Theorem #6The sum of the exterior angles of a polygon is 360°. When designing a building, exterior angles are useful because the help to position the shapes. Y = 96.5°, A = 131.2°, B = 132.3 |

## Theorem #4

Opposite* Angle Theorem: *Angle A is opposite to angle E, and angle G is opposite to B. Therefore Angle A&E must have the same angle measurements, due to the opposite angle theorem, which states that two angles opposite of each other must be the same. The same is true for angle G&B.

G&B = 86.5° each

A&E = 93.5° each

## Theorem #5

Midpoints of a Triangle: Triangle FDC is made up of 4 smaller triangles. The area of triangle FDC IS 17.6 cm2. The midpoints of this triangle spilt the triangle into four. The total are of triangle FDC is 17.6cm2, so the area of FEG, which is 1/4th must be 4.4cm2.