Download 13 Measuring and Constructing Angles

1­3 Measuring and Constructing Angles
An angle is two rays or sides sharing a common endpoint called
the vertex.
S
Symbols:
1
T
R
Q
T
1
2
R
S
Measures of angles are given in degrees. One degree is 1/360 of a
circle.
Sep 4­9:57 PM
Postulate 1-3-1: Given AB and a point O on AB, all rays that can be
drawn from O can be put into a one-to-one correspondence with the
real numbers from 0 to 180.
Types of angles:
Acute
Right
Obtuse
Straight
Sep 4­10:13 PM
1
C
80
90
100
110
70
D
60
110
50
100
90
120
80
40
130
B
140
50
130
140
30
70
60
120
40
0°
150
30
150
160
20
20
160
10
E
0
170
10
180
0
O
170
180
A
Measure and classify by type:
Congruent angles are angles that have the same measure.
C
m<ABC = m<DEF
D
So <ABC <DEF
B
F
A
E
Sep 4­10:17 PM
Construct an angle congruent to angle A
A
Postulate 1-3-2: If S is in the interior of <PQR, then
m<PQS + m<SQR = m<PQR.
L is in the interior of <JKM. Find m<JKM if m<JKL = 42o and
m<LKM = 28o.
Sep 4­10:32 PM
2
Angle bisectors are rays that divide an angle into two congruent
angles.
Construct a bisector
BD bisects <ABC. Find <ABD if m<ABD = (6x - 4)o and
m<DBC = (8x - 4)o.
Sep 4­10:37 PM
3