Words of “Wizdom”In some of the easiest problems, you will use given distances between points on a line to calculate distances between other points. This is generally a straightforward process unless you have to create your own diagram.
Try this.
Note: None of the Wizard’s figures are ever drawn to scale!
Line segment MO is 40. O is the midpoint of
MP and NO is half as long as OP.
How long is MP?
Answer #1
What is the value of ?
Answer #2
What is the value of MN + OP?
Answer #3

Parallel lines are always equal distant from one another and they will never cross each other. For example, lines l and m are parallel.

A transversal is a straight line that crosses parallel line as in the diagram above.

Vertical angles are ones that are opposite one another and equal in size. For example, y and c in the diagram are vertical angles.

Corresponding angles have the same relative position when a transversal crosses parallel lines and they are equal. For example, z and x are corresponding angles as are a and c.
If lines l and m are parallel and z equals 40 degrees,
how many degrees is x?
Answer #4
how many degrees is a?
Answer #5
how many degrees is a plus x?
Answer #6
which is larger, a + x or b + c?
Answer #7
Sample Questions
8. If lines a, b and c are parallel, how many degrees is x + y – z?
(A) 45
(B) 90
(C) 120
(D) 135
(E) 120
13. If l and m are parallel lines, which of the following must be true?
I. a + d = w + z
II. x – y = a – d
III. a + c > w + z
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) III only
Note: Figure not drawn to scale.
4. What is the value of x?
14. In the figure above, if y/3 and z/7 are integers, what is the smallest possible value of y/3 + z/7?
(A) 2
(B) 3
(C) 7
(D) 10
(E) 21
5. In the figure above, three lines intersect at a point. What is the value of 75 – a?
(A) 115
(B) 75
(C) 65
(D) 45
(E) 10
10. Four lines intersect at a point creating a set of angles that are equal. What is the size of one of the angles?
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