6.6 Symmetries of Regular
Polygons
A Solidify Understanding Task
A line that reflects a figure onto itself is called a line of symmetry. A figure that can be carried onto
itself by a rotation is said to have rotational symmetry. A diagonal of a polygon is any line
segment that connects non-consecutive vertices of the polygon.
For each of the following regular polygons, describe the rotations and reflections that carry it onto
itself: (be as specific as possible in your descriptions, such as specifying the angle of rotation)
1. An equilateral triangle
2. A square
3. A regular pentagon
4. A regular hexagon
Let the time = x
Distance = Speed x time
One train is 75x, the other train 85x
Add together to equal total distance:
75x + 85x = 384
Simplify:
160x = 384
Divide both sides by 160:
x = 384 / 160
x = 2.4 hours
Answer:
x=12
Step-by-step explanation:
Let y equal number of pushups a day. When x = 1, y = 8. When x = 2, y = 10. 10 is a factor of 30. Multiply y by 3. However, since x increases by 1 when y increases by 2, multiply x by 6 (2*3). That equals 12. Therefore, when x = 12, y = 30.
