1. Measuring Segments and Angles
Honors Geometry
Measuring Segments and Angles

2. Postulates
RULER POSTULATE
The points of a line can be put into 1 to 1 correspondence with the real numbers so that the distance between any 2 points is the absolute value of the difference of the corresponding numbers.

3. RULER POSTULATE A B
AB = |2 – 5| = 3

4. Congruent
Same measure
Notation: 
Mark up the picture with the same marks
AB  CD
A B C D
   

5. Let’s Practice    P T Q
Given:
PT = 5x + 3 and TQ = 7x – 9
Find:
PT.
x = 6, PT = 33
Answers

6. SEGMENT ADDITION POSTULATE
Postulates
SEGMENT ADDITION POSTULATE
If 3 points A, B, and C are collinear and B is between A and C, then
AB + BC = AC.

7. Let’s Practice    D S T
Given:
DT = 60 and DS = 2x – 8 and ST = 3x – 12
Find:
x, DS, & ST.
x = 16, DS = 24, ST = 36
Answers

8. Let’s Practice    E F G
Given:
EG = 100 and EF= 4x – 20 and
FG = 2x + 30
Find:
x, EF, & FG.
x = 15, EF = 40, FG = 60
Answers

9. Midpoint
A point that divides a segment into two congruent parts.
A line, a ray, or a segment can bisect another segment.

10. Bisect
Cut through at the midpoint
A line, a ray, or a segment can bisect another segment.

11. Trisect
Cut into three equal parts
A line, a ray, or a segment can trisect another segment.

12. Let’s Practice A C B   
Given
OC bisects AB, AC = 2x + 1and
CB = 3x - 4
Find:
AC, CB, & AB. O 
x = 5, AC = 11, CB = 11, AB = 22
Answers

13. Postulates PROTRACTOR POSTULATE
Let OA and OB be opposite rays in a plane. OA, OB, and all rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers 0 to 180 so that OA is paired with 0 and OB is paired with If OC is paired with x and OD is paired with y, then mCOD = |x – y|.

14. PROTRACTOR POSTULATE  O A B C D
mCOD = |x – y| = |50 – 120| = 70

15. Type Angle Range Sketch
Types of Angles
Type
Angle Range
Sketch
Acute
0 < x < 90
Right
x = 90
Obtuse
90 < x < 180
Straight
x = 180 

16. Let’s use a Ruler and a Protractor!
Complete the Measurement worksheet.

17. ANGLE ADDITION POSTULATE
Postulates
ANGLE ADDITION POSTULATE
If point B is in the interior of AOC, then mAOB + mBOC = mAOC.
If AOC is a straight angle, then mAOB + mBOC = 180.

18. Let’s Practice  W T   S  R
Given:
mRST = 50 and mRSW = 125.
Find:
mTSW
mTSW = 75
Answers

19. Let’s Practice  G    D E F
Given:
DEF is a straight angle and mDEG = 145.
Find:
mGEF
mGEF = 35
Answers

20. 5:20 4:40 6:00 Angles and the Clock
Estimate the measure of the angle formed by the hands of a clock at:
5:20
4:40
6:00
Place all three solutions here

21. Let’s Practice Q P V N M
Given:
mMQV = 90 and mVQP = 35.
Find:
mMQP
mMQP = 125
Answers

22. Let’s Practice Q P V N M
Given:
mMVQ = 55
Find:
mQVP
mQVP = 125
Answers

23. Judging by appearance, name two acute angles.
Let’s Practice Q P V N M
Place both answers here.
Judging by appearance, name two acute angles.
Judging by appearance, name two obtuse angles.

24. Let’s Practice A B C O D
Given:
mAOC = 7x – 2,mAOB = 2x + 8 and mBOC = 3x + 14.
Find: x
x = 12
Answers

25. Let’s Practice A B C O D
Given:
mAOB = 28 ,mBOC = 3x – 2 and mAOD = 6x.
Find: x
x = 18
Answers

26. Median of a Triangle
The segment joining the midpoint of a side to the opposite vertex.

27. Challenge
C is the midpoint of AB. D is the midpoint of AC. E is the midpoint of AD. F is the midpoint of ED. G is the midpoint of EF. H is the midpoint of DB.
If DC = 16, find GH.

28. GH = GF + FD + DH GH = 2 + 4 + 24 GH = 30 E G F D C H A B      32 16 16 2 E G F D 24 C H 24 A B       4 4 48 8 8