Idiot\'s Guides Basic Math and Pre-Algebra

158 Part 3: The Shape of the World

Angles ’RPQ and ’SPQ are adjacent. Angles ’ABD and ’CBD are both adjacent and linear.

P

R

Q

S

A

C

B

D

CHECK POINT

6. If m’X = 174r, then ’X is a(n) __ angle.


7. If m’T = 38r, then ’T is a(n) __.


8. If ’X and ’Y are supplementary, and m’X = 174r, then m’Y = __.


9. If ’R and ’T are complementary, and m’T = 38r, then m’R = __.


10. Lines PA and RT intersect at point Y. If m’PY R = 51r, then m’RYA = __
    and m’TYA = __.

Midpoints and Bisectors

While you’re in the middle of all these lines and segments and rays and angles, it’s a good time

to talk about middles. Because lines and rays go on forever, you can’t talk about the middle of

a line or the middle of a ray. To say where the middle of something is, you have to be able to

measure it. Until you can assign a length to an object, you can’t say where halfway is.

A midpoint is a point on a line segment that divides it into two segments of equal length, two

congruent segments. If M is the midpoint of AB, then AM~MB. Each of the little pieces is the

same length (AM = MB), and each of them is half as long as AB. Only segments have midpoints.

A line or ray or segment that passes through the midpoint of a segment is a segment bisector.

Angles don’t have midpoints, but they can have bisectors. An angle bisector is a ray from the vertex

of the angle that divides the angle into two congruent angles.