156 Part 3: The Shape of the World
When two segments have the same length, they are called congruent segments. In symbols, you
could write AB~XY to say that the segment connecting A to B is the same length as the segment
connecting X to Y. You could also write AB = XY to say the measurements—the lengths—are
the same. With the little segment above the letters, you’re talking about the segment. Without it,
you’re talking about the length, a number. Segments are congruent. Lengths are equal.DEFINITION
Two segments are congruent if they are the same length. Two angles are congruent if
they have the same measure.The same is true of angles and their measures. The symbol A refers to the actual angle, and the
symbol mA denotes the measure of that angle. If you write XYZ~ RST, you’re saying the two
angles have the same measure. You could also write mmXYZ 5 RST. Angles are congruent;
measures are equal.
A full rotation all the way around the circle is 360r. Half of that, or 180r, is the measure of a
straight angle. The straight angle takes its name from the fact that it looks like a line.
An angle of 90r, or a quarter rotation, is called a right angle. If one side of a right angle is on the
f loor, the other side stands upright. Angles between 0r and 90r are called acute angles.
Angles whose measurement in greater than 90r but less that 180r are obtuse angles.DEFINITION
A straight angle is an angle that measures 180r. A right angle is an angle that measures
90 r.
An angle that measures less than 90r is an acute angle. An obtuse angle is an angle
that measures more than 90r but less than 180r.You can classify angles one by one, according to their size, but you can also label angles based on
their relationship to one another. Sometimes the relationship is about position or location or what
the angles look like. Other times it’s just about measurements.
Two angles whose measurements total to 90r are called complementary angles. If two angles are
complementary, each is the complement of the other.
The complement of an angle of 25r can be found by subtracting the known angle, 25r, from 90r.
90 r – 25r = 65r, so an angle of 25r and an angle of 65r are complementary. To find the measure of
the complement of an angle of 12r, subtract 90r – 12r = 78r. An angle of 12r and an angle of 78r
are complementary angles.