1.4 Measuring Segments and Angles

Using a Ruler

• Length of segment:

Looking at the ruler…how long is segment CD?

CD a b Length of

3 units

**length is always the positive value of the

distance between the points

Ruler Postulate

•Postulate 1-5: Ruler Postulate

Distance between 2 points is the absolute value of their difference.

Congruent Segments

2 cm

2 cm

A B

DC

AB CD

C D

BA

AB CD

congruent segments—segments with the same length

**lengths **congruency

Ex 1: Use diagram to answer questions

a) Find the length of segment XZ 7

b) Find the length of segment XY 4

c) Find the length of segment YZ 3

d) Name 2 pairs of congruent segments

;XY ZW XZ YW

Segment Postulate

• Postulate 1-6: Segment Addition Postulate

If 3 points A, B, and C are collinear where B is between A and C, then

AB BC AC A

C

B

Ex 2: Solve for the missing variable

a)NA B

2 6x 7x25AB

2 6 7 25x x

3 1 25x

3 24x

8x

Find length of segment

AN and segment NB

10AN

15NB

Ex 2: Solve for the missing variable

b)D TS

2 8x 3 12x 60DT

2 8 3 12 60

5 20 60

5 80

16

x x

x

x

x

Find length of segment

DS and segment ST

24

36

DS

ST

Midpoint

• midpoint of a segment—the point that divides the segment into 2 congruent segments (middle point).

BA C

AB BC

Ex 3: Solve for the variable and segment lengths

a) M is the midpoint of segment RT.

Find segment lengths RM, MT, RT, and x.

MR T

5 9x 8 36x

5 9 8 36x x 45 3x

15 x

84

84

168

RM

MT

RT

Ex 3: Solve for the variable and segment lengths

b) Y is the midpoint of segment XZ and XZ = 28.

Find length of XY.

28

YX Z

14XY

Angles

• angle—formed by 2 rays with the same endpoint

1

B

A

C

vertex

side

side

Name an angle—trace angle

making sure vertex is in center

ABC

CBA

1

B

Ex 1: Naming angles

Name all the angles in the diagram

1, 2

, ,

, ,

JEN NES JES

NEJ SEN SEJ

21

E

J

N

S

Types of Angles

Acute Angle

Less than 90°

0 90x

x

Right Angle

90°

Obtuse Angle

Greater than 90°

90 180x

x

Straight Angle

x

x

180°

Angle Addition Postulate

Pretend we measured the following angles and found

these measures…

B

A

C

D

4060

What is the measure of

angle ABD?

100m ABD

Angle Addition Postulate

• Postulate 1-8: Angle Addition Postulate

1) If point B is in the interior of angle AOC, then…

m AOB m BOC m AOC

O

A

B

C

Angle Addition Postulate

• Postulate 1-8: Angle Addition Postulate

2) If angle AOC is a straight angle, then…

180m AOB m BOC

A C

B

O

Congruent Angles

• congruent angles—angles with the same measure

Notation:

1 2m m measure equal sign

1 2 no measure congruency symbol

Ex 2: Solve for the missing angle

a)

21

B

A

C

1 42

88

m

m ABC

Find 2m

b)

S

W

R

T

50

125

m RST

m RSW

Find m TSW

88 42 46

125 50 75

Ex 2: Solve for the missing angle

c)

D F

G

E

145m DEG

Find m GEF

180 145 35

HW #5: 1.4 Worksheet

HW #4: Worksheet 1-4