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MEASURING SEGMENTS AND ANGLES

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MEASURING

SEGMENTS

AND

ANGLES

Assignment

Page 29 - 30

2 – 30 even

31, 32, 34, 36, 42, 44, 46,

70, 72, 76, 78

Ruler Postulate 1- 5

The distance between any two points is the absolute value of the difference of the corresponding numbers

Example:

Length of AB is

a – b which in this

Case would be 2 – 5

Or the - 3 which is 3

B

A

Congruent segments

segments of the same length

A B C D

AB = CD or AB = CD

The two tick marks is a way of showing that the two segments are congruent

A B C D E

Compare CD and DE

CD = -2 – 0 = -2 = 2

DE = 0 – 2 = - 2 = 2

CD = DE

Segment Addition Postulate 1- 6

If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC

Example :

From previous CD = 2 and DE = 2 2 + 2 = 4

CE = -2 -2 = -4 = 4

A B C D E

4x – 202x + 30

E F G

EG = 100. Find the value of x, then EF and FG

EF + FG = EG

(4x – 20 ) + ( 2x + 30 ) = 100

6x + 10 = 100

6x = 90

x = 15

EF = 4x – 20 = 4(15) – 20 = 40

FG = 2x + 30 = 2(15)+ 30 = 60

3x +1 2x-2

E F G

EG = 64 Find EF and FG

AB = 5x + 3 and BC = 7x – 9 Find AC

A B C

Midpoint of a Segment

point that divides the segment into two

congruent segments

We are bisecting the segment

A B C

AB = BC

5x + 3 7x – 9

P T Q

Using midpoint

T is midpoint, find PT, TQ and PQ

PT = TQ definition of midpoint

5x + 3 = 7x – 9 substitution

5x + 12 = 7x add 9 to each side

12 = 2x subtract 5x from each side

6 = x divide each side by 2

PT = 5x + 3 = 5(6) + 3 = 33

TQ = 7x – 9 = 7(6) – 9 = 33

PQ = 66

Angles

two rays with the same endpoint

rays are the sides of the angle

the endpoint is the vertex

vertex

rays

A

Naming angles

D

1

2

B

<1

Use the number

<ADB

<BDA

Name the two sides with the vertex in the middle

If we were referring to <ADC we could also say that this was <D

C

Measuring Angles

Use a Protractor

Classify Angles

according to their measurement

acute

less than 90 degrees

0 < x < 90

x

Right angle

exactly 900

x = 90

Obtuse angle

greater than 900

but less than 1800

90 < x < 180

Straight angle

two opposite rays

1800

Angle Addition Postulate

If point B is in the interior of < AOC, the m<AOB + m<BOC = m <AOC

In other words, if you have two small adjacent angle they will add up to the larger angle

B

A

C

0

If < AOC is a straight angle, the m<AOB + m<BOC = 180

B

O

A

C

Try this!

If m<DEG = 145, find the m<GEF

G

D

E

F

145 + x = 180

x = 35

m< GEF = 350

Congruent Angles

Angles that has the same measure

These angles can be marked to show they are congruent