1. Section 1.4 Measuring Segments and Angles
Ms. Olifer
Geometry

2. OBJECTIVES SWBAT: Find the lengths of segments
Find the measures of angles

3. Postulate 1-5 Ruler Postulate
The distance between any two points is the absolute value of the difference of the corresponding numbers (on a number line or ruler).
Congruent Segments: two segments with the same length.

4. Geometry vs Algebra Segments are Congruent
Symbol [  ]
1  2
Lengths of segments are equal.
Symbol [ = ]
AB = CD
m1 = m2

5. Comparing Segment Lengths
Look in book for Example 1, pg 26

6. Postulate 1-6 Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C,
then AB + BC = AC C B A

7. Using the Segment Addition Postulate
If DT = 60, find the value of x. Then find DS and ST.
2x - 8
3x - 12 D S T

8. Using the Segment Addition Postulate
If EG = 100, find the value of x. Then find EF and FG.
4x - 20
2x + 30 E F G

9. Midpoint: a point that divides the segment into two equal partsB C
B is the midpoint

10. Finding Lengths C is the midpoint of AB. Find AC, CB, and AB. 2x + 1

11. Z is the midpoint of XY, and XY = 27. Find XZ.

12. Angle: formed by two rays with the same endpoint.
The endpoint is called the vertex.
Can be named by the vertex, by three letters with the vertex in the center, or by a number. A
<ABC
<CBA
<B
<1 B 1 C
*Look at example 4 in the book, pg 27

13. Postulate 1-7 Protractor Postulate
You can use a protractor to measure an angle.
*Look in book on page 28
Acute angle
< 90°
Right Angle
= 90°
Obtuse Angle
> 90° but < 180°
(90° < x < 180°)
*Example 5 on pg 28
Straight Angle
= 180°

14. Postulate 1-8 Angle Addition Postulate
If point B lies in the interior of <AOC,
then m<AOB + m<BOC = m<AOC
If <AOC is a straight angle,
then m<AOB + m<BOC = 180 A B O C B A O C

15. Using Angle Addition Postulate
What is m<TSW if m<RST = 50 and m<RSW = 125? T x W 50 R S 50

16. Using The Angle Addition Postulate
If m<DEG = 145, find m<GEF. G
145 x D E F
Congruent Angles: Angles with the same measure.