Ch. 12.5 Regular Polygons, Tessellations, and Circles

Question 1

What is a curve that can be traced with the same starting and stopping points and without crossing or retracing any part of the curve?

Answer 1

What is a simple closed curve?

Question 2

What is a simple closed curve made up of line segments?

Answer 2

What is a polygon?

Question 3

What type of polygon has all sides congruent?

Answer 3

What is an equilateral polygon?

Question 4

What type of polygon has all angles congruent?

Answer 4

What is an equiangular polygon?

Question 5

What is a polygon that is both equiangular and equilateral?

Answer 5

What is a regular polygon (regular n-gon)?

Question 6

What is the point in a polygon that is equidistant from all vertices?

Answer 6

What do we know about the center of a polygon?

Question 7

Which angle in a regular polygon (n-gon) is formed by a vertex and the two sides that have the vertex as an endpoint.

Answer 7

What is a vertex angle, also called an interior angle?

Question 8

Which angle in a regular polygon is formed by the segments joining the center of a polygon with the two endpoints of one the sides?

Answer 8

What is a central angle?

Question 9

Which angle is formed by one side together with an extension of an adjacent side of the regular polygon?

Answer 9

What is an exterior angle?

Question 10

Fill in the blanks: The number of ______ angles, _______ angles and _____ of a regular polygon are the same.

Answer 10

The number of vertex angles, central angles and sides of a regular polygon are the _____.

Question 11

Fill in the blanks: Since the central angles in a regular polygon are all congruent, one can reason ___/___ = the degrees of each central angle.

Answer 11

Since the central angles in a regular polygon are all congruent one can reason 360/n (# of sides) = the degrees of each ________ angle.

Question 12

Since all the vertex angles in a regular polygon have the same measure, one can calculate the angles by multiplying the number of _________ that can be made from one vertex by 180, then dividing it by the number of _____ in the polygon.

Answer 12

How do you calculate the vertex angles in a regular polygon using the number of triangles that can be made by one vertex and the number of sides in the polygon?

Question 13

The proper formula for calculating the vertex angle in a regular polygon is ________/_______ or __________/_________ or ___- _____/____.

Answer 13

The proper formula for calculating the _______ angle in a regular polygon is (n-2) *180/n or 180n-360/n.

Question 14

Considering the vertex angle formulas for a regular polygon, we can conclude that any vertex angle is _______ to any central angle.

Answer 14

Considering the vertex angle formulas, we can conclude that any vertex angle is supplementary to any _______ angle.

Question 15

Since the sum of a vertex angle and the exterior angle in a regular polygon is ____ degrees, each exterior angle is the same measure of the central angles.

Answer 15

Since the sum of a vertex angle and the exterior angle in a regular polygon is 180 degrees, each exterior angle is the same measure of the ______ angles.

Question 16

The formula for an exterior angle is ____/__.

Answer 16

The formula for a(n) ______ angle is 360/n.

Question 17

The formula for a ______ angle (interior angle) is (n-2)*180/n.

Answer 17

The formula for a vertex angle (interior angle) is (___-___)*___/___.

Question 18

The formula for a central angle is _____/_____.

Answer 18

The formula for a ______ angle is 360/n.

Question 19

What is a polygon together with its interior called?

Answer 19

What is a polygonal region?

Question 20

What is an arrangement of polygonal regions having only sides in common that completely covers the plane?

Answer 20

What is a tessellation?

Question 21

What are tessellations each composed of copies of one regular polygon called?

Answer 21

What are regular tessellations?

Question 22

A regular polygon will not fit together without gaps or overlapping while making a __________ if it’s vertex angle is not a divisor of 360.

Answer 22

A regular polygon will not fit together without gaps or overlapping while making a tessellation if it’s _____ angle is not a divisor of 360.

Question 23

Tessellations using two or more regular polygons that have identical vertex arrangements are called _________.

Answer 23

What are semiregular tessellations?

Question 24

Which shape is the set of all points in the plane that are a fixed distance from a given point (called the center).

Answer 24

What is a circle?

Question 25

What is the distance from the center to a point on the circle called?

Answer 25

What is a radius?

Question 26

What is any segment whose endpoints are the center and a point of the circle called?

Answer 26

What is a radius?

Question 27

What is the length of a line segment whose endpoints are on the circle and which contains the center is called the ______ of a circle.

Answer 27

What is a diameter?

Question 28

What is a device for drawing circles with different radii called?

Answer 28

What is a compass?

Question 29

A circle has _______ lines of symmetry.

Answer 29

A circle has infinitely many ______ of _______.

Question 30

A circle also has infinitely many ________ symmetries.

Answer 30

A circle has ________ many rotation symmetries.