Download Segments, Rays, Lines, and Planes

Measuring Angles
1-6
Angles

An angle is formed by two rays with the same endpoint.
The rays are the sides of the angle. The endpoint is
called the vertex of the angle.
Naming Angles

The sides of the angle shown here are BT and BQ. The
vertex is B.
You could name
the angle B,
TBQ, QBT, or
1
Naming Angles

Name
1 in two other ways.
AEC
CEA
E would not
be a correct
name, as it could
name either angle
1 or angle 2.
Degrees

Angles are measured in units called degrees.The symbol
“°” is used to indicate degrees. There are 360 degrees
in a complete circle.
360°
Degrees

Angles are measured by how many of those degrees
they take up.
This is a 90° angle
90°
270°
You would show this in writing by saying m
A=90
Angle Classifications

Angles are classified according to their measures.
This box means this is a right
angle
0<x°<90
acute
x°= 90
right
90<x°<180
x°=180
obtuse
straight
Classifying Angles
Congruent Angles
Angles with the same measure are
congruent angles.
If m
1=m
2 then
1 ≅
2
Angles can be marked as alike to show
they are congruent.
Angle Addition Postulate

If point B is on the interior of ∠AOC, then m∠ AOB +
m∠ BOC = m∠ AOC
1.
∠ RST = 50°, ∠ RSW = 125°,
2.
Find the measure of ∠ TSW
50+x=125
-50
-50
x=75
Identifying Angle Pairs
There are several pairs of angles that have special relationships:

Vertical Angles

Adjacent Angles

Complementary Angles

Supplementary Angles
Vertical Angles
1.
Two angles whose sides are
opposite rays.
2.
∠1 & ∠2 are vertical angles
3.
∠3 & ∠4 are vertical angles
Adjacent Angles
1.
Two angles who share a common
side, a common vertex, and no
common interior points.
2.
∠1 & ∠4 are adjacent angles
3.
∠3 & ∠2 are adjacent angles
4.
∠1 & ∠3 are adjacent angles
5.
∠2 & ∠4 are adjacent angles
Complementary Angles
1.
Two angles whose
measures equal 90°
2.
∠XYW+∠WYZ = 90°
Supplementary Angles
1.
2.
Two angles whose
measures equal 180°
∠XYW+∠WYZ = 180°
Identifying Angle Pairs

Identify the angle pairs:
a.
Vertical
b.
Complementary
c.
Supplementary
Making Conclusions from Diagrams
Unless there are markings given, you cannot assume anything.
Making Conclusions from
Diagrams

What can you conclude from the following diagram?
Making Conclusions from
Diagrams

Can you make the following conclusions based on this diagram?
TW ≅ WV?
PW ≅ WQ?
∠TWQ= 90°?
W is the midpoint of TV?
TV bisects PQ?
Coordinate Plane
1-8
Coordinate Plane
Coordinate Plane
Points are located on a coordinate plane by using an ordered pair. (x,y)
called the coordinates.
T = ( 5,2 )
R = ( -4,-1 )
Distance Formula
T = ( 5,2 )
R = ( -4,-1 )
D=√(x2-x1)2 + (y2-y1)2
D=√(-4-5)2 + (-1-2)2
D=√(-9)2 + (-3)2
D=√81 + 9
D=√90
D=9.486832981
D=9.5
Midpoint Formula

Find the midpoint of a segment by
averaging the x-coordinates and
averaging the y coordinates of the
endpoints.
x1+x2
2
, y +y
1
2
2
Finding the Midpoint
Find the midpoint.
x1+x2 , y1+y2
2
2
3+7 , 5+(-5)
2
2
10 , 0
2 2
(5,0)
Finding the Midpoint

The endpoints of XY are X(2,-5) and Y(6,13). Find the
coordinates of the midpoint.
Finding the Endpoint

The midpoint of AB is M(3,4). One endpoint is A(-3,-2).
Find the coordinates of B.
Finding the Endpoint
The
midpoint of XY
is (4,-6). X is (2,-3).
Find the coordinates
of Y.
Worksheets

1-6: Complete 1-15

1-8: Complete 1-25

Due Tomorrow