This unit focused, in part, on relationships in triangles. a triangle is the simplest type of polygon and is frequently used in construction. explain why triangles are often used to build bridges, roofs, buildings, and other structures. which properties of a triangle make it a desirable geometric shape for these applications? which type of triangle is best? why is the triangle preferred over other types of polygons? explain.

A triangle is the strongest polygon. It is frequently used in construction because of its ability to distribute weight equally and withstand the force without any deformation.

Property of triangle that makes it a desirable geometric shape :The angle of the triangle is dependent on the side of the triangle opposite to it.

Once the triangle is constructed, there is no change in the angle between the legs unlike other polygons. This is mainly because the angle depends on the length of the side of the triangle. This the reason why triangles are preferred over other polygons. Also, any polygon can be strengthen by splitting it into triangles.

Equilateral triangles are most commonly used in truss bridges. Another most common triangle used in designing is right angled triangle.  

The answers are as follows:

1. Triangles are often used to build different types of support structures because of its beneficial properties. Triangles is rigid in shape and it has strength. When force is applied to the side of a triangle, it can not shift into another shape, this is because its sides and angles are fixed. 

2. The properties of triangle that make it a desirable geometric shape for building support structures is its fixed sides, fixed angles, rigidity and strength. Triangles are the strongest shapes and they are stable. Thus, triangle can be easily fix together to provide strength and stability over a wide area.

3. There are different types of triangles, these include: equilateral triangle, scalene, isosceles, right triangle, obtuse and acute. Of all these triangles, the best triangle is equilateral triangle.  

4. Triangle is preferred over other types of polygon because, it is the strongest. The other polygons can be bent into different other forms that are not regular polygon, but a triangle always retains its shape and can not be deformed.

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two