EXAM 2
366-504
Mar. 30

Name
SSN

Section I. For each of these problems circle the correct answer. You may support your reasons if you so desire. (4 pts each)

1. A rigid motion takes a plane figure to another plane figure of the same shape, though the size may grow or shrink.
   1. True
   2. False
2. If two figures are congruent then corresponding angles are identical and corresponding sides have the same ratio but not necessarily the same length.
   1. True
   2. False
3. The number eight has only one line of symmetry.
   1. True
   2. False
4. A regular octagon has rotation symmetry about its center.
   1. True
   2. False
5. Suppose you have a pair of triangles and that you know these triangles have two corresponding sides which are the same length, and that they have corresponding angles which are congruent. Assume the angle is not between the two known sides. These triangles must be congruent.
   1. True
   2. False
6. Which of the following is not necessarily a property of a rhombus.
   1. The diagonals bisect one another.
   2. It is a rectangle.
   3. It is a parallelogram.
   4. The sides are all congruent.
   5. The diagonals are perpendicular.
7. Two triangles are similar if and only if at least two corresponding angles are congruent.
   1. True
   2. False
8. A triangle has two sides of lengths 10 and 16. Which of the following numbers CANNOT be the length of the other side.
   1. 11
   2. 25
   3. 1
   4. 20

Section II. In each of the following problems you must support your answer. You need not write every detail, but you must show how you got your answer.

1. Construct a triangle with one side congruent to the line segment and one angle congruent to . (7 pts)

   

2. For each of the following figures complete the indicate symmetry (either point or line). (7 pts)
   

   

3. Construct a line parallel to which passes through C and construct a line perpendicular to which passes through F. (8 pts) passes through the given point.
   
   
   

   

4. Construct a square which has a side length congruent to the following line segment. Then construct an octagon with a diameter which is congruent to the line segment. (10 pts)
   

   

5. Suppose is an isosceles triangle. It has the property that the circular arc centered at A intersects the opposite side at a point D for which . Use this property, together with the fact that the dashed line is parallel to to find the measures of the angles of . (9 pts)
   

   

6. In each of the following figures find each pair of congruent triangles. (10 pts)
   
   
   

   

   
   
   
   
   
   

7. In the following figure, ABCD is a square and . What kind of figure is AECF? Prove it. (Hint: Two lines are parallel if and only if opposite interior angles, or corresponding angles, are congruent. 9 pts)

   

8. On the attached sheet of graph paper find the line of reflection and the slide arrow that will send B to B' and E to E'. Then draw the polygon in its new position. (8 pts)

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