http://www.ck12.org Chapter 1. Basics of Geometry
Polygons can be eitherconvexorconcave. A concave polygon has a section that “points inward” toward the middle
of the shape.Diagonalsare line segments that connect the vertices of a convex polygon that are not sides.
Guided Practice
Name the three polygons below by their number of sides and if it is convex or concave.
Answers:
A. This shape has six sides and concave, so it is a concave hexagon.
B. This shape has five sides and is convex, so it is a convex pentagon.
C. This shape has ten sides and is convex, so it is a convex decagon.
Practice
In problems 1-6, name each polygon in as much detail as possible.
1.
2.
3.
4.
5.
6.
- Explain why the following figures are NOT polygons:
- How many diagonals can you draw fromone vertexof a pentagon? Draw a sketch of your answer.
- How many diagonals can you draw fromone vertexof an octagon? Draw a sketch of your answer.
- How many diagonals can you draw fromone vertexof a dodecagon?
- Use your answers from 8-10 to figure out how many diagonals you can draw fromone vertexof ann−gon?
- Determine the number of total diagonals for an octagon, nonagon, decagon, undecagon, and dodecagon. Do
you see a pattern? BONUS: Find the equation of the total number of diagonals for ann−gon.
For 13-17, determine if the statement is ALWAYS true, SOMETIMES true, or NEVER true.
- A polygon must be enclosed.
- A star is a concave polygon.
- A quadrilateral is a square.
- You can draw(n− 1 )triangles from one vertex of a polygon.
- A decagon is a 5-point star.
In geometry it is important to know the difference between a sketch, a drawing and a construction. A sketch is
usually drawn free-hand and marked with the appropriate congruence markings or labeled with measurement. It
may or may not be drawn to scale. A drawing is made using a ruler, protractor or compass and should be made to
scale. A construction is made using only a compass and ruler and should be made to scale.
For 18-21, draw, sketch or construct the indicated figures.
- Sketch a convex heptagon with two sides congruent and three angles congruent.
- Sketch a non-polygon figure.
- Draw a concave pentagon with exactly two right angles and at least two congruent sides.
- Draw an equilateral quadrilateral that is NOT a square.