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Lesson 3 : (1.5 ) Measuring Segments (1.6) Measuring Angles. “Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.” -Ann Landers. What are we learning?. Students will…

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Lesson 3: (1.5)Measuring Segments (1.6) Measuring Angles

“Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.”

-Ann Landers


What are we learning?

  • Students will…

    • find the measures of segments as well as angles using the segment addition and the angle addition postulates.

Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a)

Purpose (Relevancy): The highway can be seen as a number line. By applying the segment addition postulate, a person could find the distance from one exit to another.


Postulate 1-5

The Ruler Postulate: The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers

The distance between points A and B on the ruler is 7. To find the length of AB, find the absolute value of the difference of the coordinates of A and B, called “a” and “b.”

AB = |a - b|

A

B


Postulate 1-5

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

Example: Using AB = |a - b|

Find:

DE

EG

DG

E

G

D

-7

5

-2

0


Congruence

Congruent Segments: Segments that have the same length

Example: Which of the following are congruent? How do we show congruence?

If AB = CD, then AB ≅ CD

AB ≅ CD

=

B

3 in.

=

C

4 in.

A

3 in.

E

F

D


Postulate 1-6

Segment Addition Postulate: If 3 points, A, B, and C, are collinear and B is between A and C, then AB + BC = AC

A

B

C

Example: If XZ = 88, find the value of x. Then find the values of XY and YZ

3x - 2

4x + 6

X

Y

Z


Types of Angles

Acute Angle: less than 90°

Right Angle: Exactly 90°

Straight Angle: exactly 180°

Obtuse Angle: more than 90°


Postulate 1 - 8

Angle Addition:If point B is in the interior

Of <AOC, then <AOB + <BOC = <AOC

B

A

O

C

Example:If <POW is 97°and <POQ is 29o, what is <QOW

Q

P

W

O


Lesson 3: (1.5) Measuring Segments (1.6) Measuring Angles

HW: Pgs. 33-34; 6-14 e, 20-23, 35-37

Pgs. 40-41; 1-14 a

“Keep in mind that the true measure of an individual is how he treats a person who can do him absolutely no good.”

-Ann Landers


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