EXAM 3
366-504
April 27

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. Any two isosceles triangles must be similar.
   1. True
   2. False
2. Any two equilateral triangles must be congruent.
   1. True
   2. False
3. If two triangles have two congruent sides and one congruent angle (which is not necessarily included between the two congruent sides) then the triangles are congruent. (SSA)
   1. True
   2. False
4. The line 2x+3y=6 has a slope of 2.
   1. True
   2. False
5. The equation defines a circle with the center at (3,5) and a radius of 9.
   1. True
   2. False
6. Which of the following conditions do NOT completely describe a triangle
   1. Side-Angle-Side (SAS)
   2. Side-Side-Side (SSS)
   3. Angle-Side-Angle (ASA)
   4. Side-Side-Angle (SSA)
   5. Angle-Angle-Side (AAS)
7. 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. 30
8. Choose the line which is parallel to y=5x-10.
   1. y=23x+7
   2. 3y=15x+9
   3. 10y=7x-1
   4. -y=3x+2
9. Two convex quadrilaterals and , have congruent angles at there corresponding vertices: and It follows that these quadrilaterals must be similar.
   1. True
   2. False
10. Suppose two convex quadrilaterals have corresponding sides in the same ratio. Then these quadrilaterals must be similar.
    1. True
    2. False
11. The vertical line test states that if any vertical line intersects a graph more than once then the graph is the graph of some function.
    1. True
    2. False

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. (6 pts each)

1. Are the lines 2x-3y=7 and -6x+2y=2 parallel? Perpendicular? Neither? If they are not parallel find their point of intersection.

2. Construct a triangle with one side congruent to the line segment and an angle congruent to .

   

3. In each of the following figures find each pair of congruent triangles.
   

   

   
   
   
   

4. Graph the function on the following axes, then find the minimum value of the function.
   

   

5. Construct a line parallel to which passes through C and construct a line perpendicular to which passes through F. passes through the given point.
   

   

Section III. In the following problems you need to describe your thought processes. Try to be concise. (7 pts each)

1. Assume that is a Rhombus and prove that M is the midpoint of and
   
   
   
   

   

2. Use coordinates to write down the equations of the perpendicular bisectors for each side of the triangle below. Show that these lines are concurrent (have a single point of intersection).
   

   

   
   
   
   

3. Construct a regular hexagon whose ``diameter'' is congruent to the line segment .
   

   

4. Construct an angle which measures without using a protractor.

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