# Investigation 1

Main Topics: What is a polygon, How to measure angles, How to draw polygons

What is a Polygon? A polygon is a shape with at least 3 sides and angles. It has all side angles connected, no round sides, and no intersecting sides.

How to measure an angle: To measure an angle, you need a tool called a protractor, place the circle in the middle of the protractor on the vortex; the meeting point of two lines to form an angle, and look at the way the line or side the protractor is on. Follow it until you see zero. Once you see zero go up until you are at the angle. See what the measurement it is pointing to and that is the degree of the angle. Some common benchmark angles are 90 degrees, 60 degrees, 30 degrees, 45 degrees, 120 degrees, 150 degrees and 360 degrees. Many of these angles can be found in quadrants. In a quadrant, you can use rotation to make angles. You can rotate a line from point 0 and make it go to point 3. This makes a 30 degree angle.

How to draw polygons:To draw a polygon (triangle)triangle ABC with AB=1 inch,BC=5 inch, angle CBA=35. To start the triangle draw a dot to represent a.Then draw a line represents B. After that  ,using your protractor, make a point at 35 and B with a 1.5 long line (BC and CBA). To finish the triangle make a line connecting the 35 angles (C). And there you have your polygon.

Supplementary and Complementary angles:Many types of angles can be put together to make another type of angles. The to most common ones are: supplementary and complementary angles. Supplementary angles are two angles that for a straight line (180 degrees). They are always next to each other. Complementary are very similar but instead of the two angles sum equaling 180 degrees these are 90 degrees.(a right angle)

# Investigation 2

Main topics: Regular & Irregular polygons; number of sides related to the sum of interior angles in a polygon; sum of exterior angles.

Regular & Irregular: A regular polygon has sides that are the same length and angles that are the same measure. An irregular polygon doesn't have sides that are the same length and not all angles have the same measure.

Some regular polygons can cover a plane surface with geometric shapes with no overlaps or gaps. This is called tiling or tessellation. Honeybees build nests using tiling.

Irregular polygons can be concave or convex polygons. Convex polygons have interior angles measuring less than 180 degrees. concave polygons have at least one interior angle whose measure is greater than 180 degrees.  Also, by extending a side of a convex polygon, you can make an exterior angle that lies outside of the polygon. Measuring exterior angles is very easy useful in in finding the measure of the interior angles. # of sides is related to the sum at the interior angles.

In finding the sum of all the interior angles we have come up with two formulas: 100 X (n-2) and 180Xn -360. Both of the formulas have been tested and they both.

# Investigation 3

Main topics: how mach into is needed to copy a triangle and a quad, why are triangles so useful in building structures and what is the problem with quads in building,traversal and vertical angles, symmetry.

How much information is need to copy a triangle and a quad ?

Building a triangle to match another one can be hard. most of the time you need certain requirements to make it. Here are the 3 we know AF: 2 side lengths and an angle; two angles and a side length; or three side lengths. It is pretty much the same with a quadrilateral them it a little different thought. Here's how; Three side lengths and an angle;Three angles and a side or four side lengths.

Why are triangles so useful in building?

Why are triangles so useful in building? And why are quadrilaterals so bad at being in building structures? Well triangles are so useful is because they're the strongest shape for building. If you put pressure on them they don't calopes like a quadrilaterals(busy quadrilaterals)

Traversal and vertical angles

A line that intersects two other( or more)is called a traversal. Traversal lines are mostly likely seven in the world as a train track so, vertical angles do connect to traversal though literally! When to lines intersect four angles are formed, the opposite pairs of angles are called vertical angles

Symmetry

So, what even is symmetry. well the most common forms of symmetry are reflection symmetry and rotational symmetry. Reflection symmetry is just as simple as it sounds. It's like a mirror. The polygon is split into two halves and the mirror each other. Rotational symmetry is when you turn a shape, between zero examples at this are rectangles for rotational and a diamond for reflection .