Geometry - Polygons

12 important questions on Geometry - Polygons

What on earth is a polygon?

A polygon is any closed figure with all-line segment sides.

What are the 3 reasons that exclude a polygon from being polygon (in other words, if it has any of these properties its NOT a polygon)?

A) the figure does not close
B) the sides cross
c) not all sides are straight

What on earth are "concave" polygons?

Essentially the opposite of convex polygons.
Convex polygons: every vertex pointed outwards.
font-weightConcave polygons: one or more vertices (plural of vertex) pointed inwards.
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How do you call a polygon with 4 sides?

A polygon with 4 sides = a quadrilateral

Recall: how is a diagonal defined?

A diagonal is defined as "any segment that connects two non-adjacent vertices"

How many diagonals do triangles have?

None

How many diagonals do Quadrilaterals have?

Quadrilaterals have 2 diagonals

How many diagonals do pentagons have?

Pentagons have 5 diagonals.

How many diagonals do hexagons have?

Hexagons have 9 diagonals

To how many degrees do the interior angles in a pentagon always add up to?

The angles in a pentagon always add up to 540.

True or false: any pentagon can be broken down into 3 triangles

True, this is also how you can reason your way to the todal degrees in a pentagon: triangles add up to 180, 3 triangles in a pentagon = 3*180 = 540

True or false: any hexagon (6 sides) can be broken up into 4 triangles. If so, what is the total sum of angles?

True, because of that we can reason as follows: a triangle adds up to 180 degrees, 4*180 = 720 degrees. Every hexagon has 720 degrees.

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