Download section 1-3 Measuring and Constructing Angles angle

Measuring and Constructing Angles
section 1-3
angle - a figure formed by two rays (sides) with a common endpoint
(vertex) (the plural is vertices). An angle can be named by its
vertex, by a point on each ray plus the vertex, or by a number.
A
X
2
or
or
AXB
2
B
X
A
C
AXB
or
2
but not
X
X
Why not?
2
B
Angles can be measured on paper with a protractor or in the
three-dimensional world with a transit.
Angles are measured in units called degrees. Since a circle
contains 360 , then each degree comprises 1/360 th of the circle.
You can use the Protractor Postulate to help you classify angles
by their measure. The measure of an angle is the absolute value
of the difference of the real numbers that the rays correspond
with on a protractor.
If OC corresponds with c and
OD corresponds with d, then
m DOC = |d – c| or |c – d|.
problem # 1 - Find the measure of each angle below and decide
whether it is acute, right, or obtuse.
a.
YXW
b.
YXZ
c.
UXW
U
congruent angles - angles that have the same measure.
* In a diagram, arc marks may be used to indicate that two angles
are congruent.
P
A
AXB
X
PYQ
Q
B
Y
* The Angle Addition Postulate is very similar to the Segment
Addition Postulate that we learned in the last lesson.
problem # 2 - m
DEG = 115°, and m
DEF = 48°. Find m
FEG.
angle bisector - a ray that divides an angle into two congruent angles.
JK bisects
LJK
LJM. Therefore,
KJM.
problem # 3 - KM bisects JKL, m JKM = (4x + 6)°, and
m MKL = (7x – 12)°. Find m JKM.
Constructing a Congruent Angle
Constructing an Angle Bisector