1. Section 1-4: Measuring Segments and Angles
Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems.

2. Essential Questions
1.) How do you find the length of a segment on a number line?
2.) How do the midpoint and bisector of a segment differ?
3.) How are angles identified and classified?

3. length of a segment
the distance between two points P and Q, denoted PQ or QP, on a number line is the absolute value of the difference of their coordinates.
P coordinate – Q coordinate  or
Q coordinate – P coordinate 

4. congruent segments segments that have equal length
 is read segment DE is congruent to segment FG

5. midpoint of a segment
the point that divides a segment into two congruent segments

6. bisector of a segment
a line, ray, segment, or plane that intersects the segment at its midpoint

7. angle the union of two rays which have the same endpoint
The two rays are called the sides of the angle. (Use rays to name the sides of angles and the endpoint must be the vertex.) Their common endpoint is the vertex.

8. angle
Three sets of points make up an angle: the interior, exterior, and the angle itself.
The symbol  is used for an angle. Usually three capital letters are used to name an angle (may use a number or the vertex as a single letter). Never use only two letters to name an angle. If using three letters, use a letter on the two different sides of the angle.

9. acute angle
an angle with degree measure m such that
0 < m < 90

10. right angle
an angle with degree measure m = 90. (Use a little box in the vertex of the angle to indicate a right angle on a diagram.)

11. obtuse angle an angle with degree measure m such that

12. straight angle
an angle with degree measure m = 180

13. congruent angles angles that have equal measures
For example:  1   2 means m  1  m  2
*Note: Indicate that angles are congruent on a diagram by drawing an arc at the vertex in
the interior of the angles with a corresponding number of tick marks (slashes) through the arcs.

14. Examples P. 29, 30
1, 3
DO 2, 4 5
DO 6, 7 12
DO 14
Pairs do p 30 (16 – 26)

15. Segment Addition Postulate
B is between A and C iff AB + BC = AC.
A B C

16. 8) If RS = 15 and ST = 9, then RT =
10) a. If RS = 3x + 1, ST = 2x – 2, RT = 64. Find x. b. Find RS and ST.
Do 9, 11

17. Angle Addition Postulate
If point B lies in the interior of  AOC,
then m  AOB + m  BOC = m  AOC. A B O C

18. 27) Find m<CBD if m<ABC = 45 and m< ABD = 79.
28) Find m<GFJ if m<EFG = 110.
Do p 31 (42 – 48, 65, 66)

19. Homework
Practice 1-4
Mixed review, p 33 (87 – 97)