Lesson 3Lesson 3: (1.5) Measuring Segments : (1.5) Measuring Segments (1.6) Measuring Angles(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 1-5Postulate 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

AABB

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|

Postulate 1-5Postulate 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

D E G

5 -2 -7 0

Congruence

Congruent Segments: Segments that have the same length

If AB = CD, then AB CD ≅Example:

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

3 in.

A

B

3 in.

D

C

EF

4 in.

=

=

AB ≅ CD

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

Postulate 1-6

A

B

C

X Y Z

3x - 2 4x + 6

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

Types of Angles

Acute Angle: less than 90° Right Angle: Exactly 90°

Obtuse Angle: more than 90° Straight Angle: exactly 180°

Postulate 1 - 8

Angle Addition:If point B is in the interior Of <AOC, then <AOB + <BOC = <AOC

O C

BA

P

O

Q

W

Example:

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

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

HW: Pgs. 33-34; 6-14 e, 20-23, 35-37 Pgs. 40-41; 1-14 a