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Warm-up

- Fill in the blank with always, sometimes, or never.
- Explain your answer.
- A bisector of a segment is ______ a line.
- A ray ______ has a midpoint.
- 3. Congruent segments ______ have equal lengths.
- 4. If B is between A and C, then AB ________ equals BC.

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Lesson 1-4 Angles

angle () – a figure formed by two rays that have the same endpoint. The two rays are called sides of the angle.

Their common endpoint is called the vertex.

Angle name(s)

Sides

Vertex

acute angle– an angle with measure between 0 and 90.

obtuse angle– an angle with measure between 90 and 180.

right angle– an angle with measure 90.

straight angle– an angle with measure 180.

Postulate 3 Protractor Postulate

On AB in a given plane, choose any point O between A and B.

Consider OA and OB and all the rays that can be drawn from

O on one side of AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:

a. OA is paired with 0, and OB with 180.

b. If OP is paired with x, and OQ with y, then POQ = |x – y|.

P

x

Q

y

A

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B

Use a protractor to measure each angle to the nearest degree. Then,write three names for each angle.

B

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A

If AOC is a straight angle and B is any point

not on AC,then

B

O

A

C

Postulate 4Angle Addition Postulate

If point B lies in the interior of AOC,then

mAOB + mBOC = mAOC .

mAOB + mBOC = 180 .

35

35

A

Lesson 1-4 Angles (continued)

congruent angles– angles that have equal measures.

congruence marks

If mA = mB, then A B.

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adjacent angles (adj. s)– two angles in a plane that have a common vertex and a common side but no common interior points.

1 and 2 are adjacent angles.

3 and 4 are NOT adjacent angles.

O

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If NO bisects MNP, then ___________

bisector of an angle– the ray that divides the angle into two congruent adjacent angles.

MNO ONP.

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Ex. 1) Find each angle measure, given the diagram and information below.

Given: m1 = 5x,

m2 = (x + 40), and

m3 = (x2 – 20)

Ex. 2) Given that AM bisects LAR and AS bisects MAR, find mLAR using the given information.

Given:mRAM = (5x – 7), and

mMAS = (x + 3)

HOMEWORK#5

page 22 29-36 all

Read pages 22-23 and complete the outline of Lesson 1-5, including allvocabulary, postulates and theorems

(but NOT the warm-up, examples, or cool-down.

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