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1-4 Warmup

Simplify each absolute value expression.

1) –62) 3.53) 7 – 10

4) –4 – 25) –2 – (–4)6) –3 + 12

Solve each equation.

7. x + 2x – 6 = 6

8. 3x + 9 + 5x = 81

9. w – 2 = –4 + 7w

Lesson 1-4: Measuring Segments & Angles

The location of a point.

Objects that are the same shape and size

A point that divides a segment into two equal segments

Formed by two rays or segments that share an endpoint

An angle whose measure is smaller than a “corner”

An angle whose measure is a “corner” - 900

An angle whose measure is greater than a “corner”

An angle whose measure is a straight line - 1800

Measures with segments:

Distance between two points is the absolute value of the difference between their coordinates.

A

B

-1

0

1

Distance from A to B is or

Both equal 9!

Example 3-1a

Use the number line to find QR.

The coordinates of Q and R are –6 and –3.

Distance Formula

Simplify.

Answer: 3

(cont’d)

- Symbol:
AB means the segment:

AB (without symbol) means the length

- Congruent segments
- When 2 segments are the same length, we write…

or

A

C

B

D

Small segment

Whole segment

- Segment Addition: “parts of a segment add to the whole”
___________ + ___________ = ____________

- Midpoint
- Forms 2 congruent segments on a segment (Cuts it in half!)
- Equations:
________ = _________

________ = ½ ● ________

These red marks indicate segments AM and BM are the same.

A

M

B

Small segment

Other small segment

Small segment

Whole segment

Multiple-Choice Test ItemWhat is the measure of ifBis the midpoint of ?

A 1 B 3 C 5 D 10

Example 3-5eAnswer: D

Angles

A

vertex

1

sides

B

C

Parts:

Sides: rays BA and BC

Vertex: point B

Naming:

3 letters (all angles):

1 letter:

1 number:

Tracing these letters makes the angle.

or

Only when there is exactly 1 angle at the vertex!

a. Name all angles that have X as a vertex.

b. Name the sides of 3.

Answer:

c. Write another name for 3.

Example 4-1dAnswer:1, 2, 3, and RXB or RXN

Answer:AXB, AXN, NXA, BXA

Types of angles

- Acute – “small”
- Measures 00 - 890

- Right – “right turn”
- Measures 900

- Obtuse – “obese”
- Measures 910 - 1790

- Straight
- Measures 1800

This red box indicates a right angle of 90 degrees.

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