Angles and Segments

1
Lesson 1-3

• Angles and Segments

2
Segments

• Can determine the length of segments
• On a number line, subtract the coordinates and
  take the absolute value
• Example
• What are the coordinates of the endpoints?
• What do you get when you subtract?
• How do you take the absolute value?
• What is the measure of segment AB?

3
Segment Addition Postulate

• If A is between B and C
• Then BA AC BC
• Example Problems
• Practice pg. 21 s 19, 21, 23, and 25

4
Using Algebra to Solve for Length

• Example Problem
• Practice pg. 22 s 31 and 33

5
Midpoint

• On a number line
• Add the coordinates and divide by 2
• On the coordinate plane
• Do the same thing but do x and y separately
• Answer will be a point so put in parentheses
• Formula

6
Congruent

• The midpoint of a segment splits the segment into
  two congruent segments
• An angle bisector splits the angle into 2
  congruent angles
• Congruent is just a fancy word for equal
• Can use distance formula to determine whether
  segments are congruent
• Practice pg. 22 s 41 and 43

7
Angles

• Angles are created when 2 rays share an initial
  point
• The shared initial point is called the vertex and
  the 2 rays create the 2 sides of the angle
• QUES IS A LINE AN ANGLE????

8
Given Angle A

• Name the vertex
• Name the 2 sides

9
Naming Angles

• You can name an angle just by the vertex if only
  one angle is shown
• You must use 3 letters and put the vertex in the
  middle if more than one angle shares the same
  vertex

10
Which of the following can be named with a single
letter?

• A.)
• B.)

• C.)
• D)

11
Name all numbered angles shown

• A.)
• B.)

12
Measuring Angles

• Use a protractor
• Measured in degrees
• Line up the vertex and 1 side
• Read the protractor
• Two rows of numbers
• Use logic!!!!
• If it looks bigger than 90, use the big number
• Know acute, obtuse, right, straight definition
• Symbol for right triangle
• Website

13
Angle Addition Postulate

• Example
• Angle 1 Angle 2 Angle ABC

14
Angle Addition Example Problem

• Calculate x _______
• Find the measure of Angle ABD _______
• Find the measure of Angle DBC _______

A
D
2x-3
3x1
B
C
15
Angle Bisector

• Basically a ray that splits the angle into 2
  equal parts
• Can use symbols/marks to indicate that angles are
  equal

16
Complementary and Supplementary Angles

• Complementary Add up to 90
• Supplementary Add up to 180 (Straight Line)

17
Linear Pair

• Two adjacent angles are a linear pair if their
  non common sides are opposite rays
• Basically, if 2 angles make a line or add up to
  180 degrees, they form a linear pair

18
Vertical Angles

• Two angles are vertical angles if their sides
  form two pairs of opposite rays
• Angles 1 and 3 are vertical angles
• Angles 2 and 4 are vertical angles