Words of “Wiz-dom”-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.
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?
What is the value of ?
What is the value of MN + OP?
Words of “Wiz-dom”-Remember:
360o around a point
Parallel lines are always equal distant from one another and they will never cross each other. For example, lines l and m are parallel.
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?
how many degrees is a?
how many degrees is a plus x?
which is larger, a + x or b + c?
8. If lines a, b and c are parallel, how many degrees is x + y – z?
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?
5. In the figure above, three lines intersect at a point. What is the value of 75 – a?
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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