Math 192, Exam III
Name _____________________________
There are 13 problems on this exam. Only those problems that say “explain” require
explanations. Answers that require explanations will be given at most half credit without
the required explanation. Be sure to follow all directions.
Use the following diagram for problems 1-5. Use a different color for each problem.
(5 points each)
1. Draw the image of hexagon ABCDEF when it is translated using the indicated
translation vector. Label your image as GHIJKL.
2. Draw the image of hexagon ABCDEF when it is reflected using line m as the line of
reflection. Label your image as MNOPQR.
3. Draw the image of hexagon MNOPQR when it is reflected using line n as the line of
reflection. Label your image as STUVWX.
4. Draw the image of hexagon ABCDEF when it is rotated 90 clockwise about point Y.
Label your image as ABCDEF .
5. What single transformation will take hexagon ABCDEF to hexagon STUVWX?
If it is a translation show the translation vector. If it is a rotation specify the angle and
direction of the rotation. If it is a reflection specify the line of reflection.
6. Draw a hexagon that is similar to hexagon ABCDE shown below using a scale factor
k = 3. (5 points)
A
B
D
C
F E
7. What is the ratio of the area of hexagon ABCDEF to the area of the hexagon in
problem 6? (3 points)
8. Determine the line and rotational symmetry of the following figure. (8 points)
9. Use a MIRA to determine the incenter for the following triangle and then draw the
inscribed circle. (10 points)
10. The image of quadrilateral ABCD under a rotation is shown below.
(a) Use paper folding to locate the center of rotation. (10 points)
A'
D'
A
B
B'
C'
D
C
(b) What is the angle of rotation? Is the rotation clockwise or counterclockwise? (5 pts)
11. (a) Draw ABC if mAC  4.8 cm, mBCA  75 , and mBC  5.8 cm. (10 points)
(b) What theorem guarantees that the triangle you drew in part (a) will be congruent
to the triangle I drew on the exam key? (3 points)
12. Use the F, L, N, P, T, and U from your pentomino puzzle pieces to make a 5  6
rectangle. Use a different color for each pentomino piece and graph your answer on
the grid below. If you cannot solve this puzzle with the six pieces I specified, you
can interchange one piece for half credit. (10 points)
13. In the following diagram line AE is perpendicular to line BD and line AB is
parallel to line DE . Use appropriate notation to list the pair of similar triangles and
explain why they must be similar. (5 points) Then show all work necessary to
determine the value of x. (10 points).
A
72 cm
x
B
C
24 cm
40 cm
E
D