1.12. Polygon Classification http://www.ck12.org
- 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.
Summary
This chapter begins with the basic components of Euclidean Geometry. From the introductory definition of points,
lines, and planes it builds to a discussion of classifying figures such as angles, triangles, and polygons. Measurement
of distances and angles are also covered. Different types of angle relationships are compared and explored, such as
complementary angles, supplementary angles and linear pairs.
Symbol Toolbox for Chapter
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AB,ABLine, ray, line segment(^6) ABCAngle with vertexB
mABorABDistance betweenAandB
m^6 ABCMeasure of^6 ABC