Geometry
Chapter 1 Review
1. A regular figure has rotational symmetry about its center so that every time it is rotated 72° it looks exactly the same. What is the minimum number of sides this figure must have. What is that figure called? Justify your reasoning.
2. Reflect across the y–axis and label the
image . Reflect the image now across
the x-axis. Label the new image .
A single transformation from to
can be achieved by rotating the original figure.
Where is the center of rotation and how many
degrees was the triangle rotated?
3. Write in a simpler, shorter form without parentheses:
-2(3x – 5) + 2x – 2(5 – x)
4. a. Solve for x: 5x + 6 = 31 b. Simplify: 3(x + 2) - 4x.
5. Solve for x.
6. If 3x + 4 = y and 2x – 2y = -12, solve for x and y.
7. A regular hexagon has rotational symmetry about its center. What is the minimum number of degrees of rotation necessary to show rotational symmetry? Explain your reasoning using math vocabulary.
8. For each figure, draw the transformation described.
a. Reflect ABCD across line l b. Rotate DPQR 90° clockwise ( P )
about the origin.
9. Examine the rectangle at right. If the perimeter of this shape is 90 cm, which equation below represents this fact? Once you have selected the appropriate equation, solve for x.
a. b.
c. d.
10. There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word geometry?
11. For a standard deck of cards, what is the probability of drawing a card smaller than a 10? (Aces are high.)
12. If your birthday is in May (which has 31 days), what is the probability it is on an even numbered day?
13. Fill in the chart for each equation.
Equation / Slope / Y-intercepty = x – 4
y = -x + 5
y – 2x = 7
Graph the first two equations on this grid.