Chapter 1-4 Angles and Segments

To Use and apply the Segment Addition Postulate and Angle Addition Postulate

To classify angles

1.4 Congruent Segments and Congruent Angles

If 2 segments are ≅, they are = in length.

If 2 angles are ≅, they are equal in size.

A B C D E F G H

-9 -7 -2 0 2 3 6 9

Measuring & comparing segments

Compare

1. AB ___ EF 2. BC____EG

3. CD ___DE

Segment Addition Postulate

A B C

AB + BC = AC

i.e. the parts = the whole

M A N

1. If MA = 12 and AN = 11, then MN =______

2. If MN = 38 and AN = 22,

then MA = ______

A B C2X + 5 3X - 2

AC = 38Find x, AB,& BC.

MN = 8 MO=21Find the coordinatesof N and O.NO = _____

M N O-12

Midpoint of a segment

A point that divides a segment into 2 congruent parts.

Segment Bisector

A line, line segment, ray or plane that intersects a segment at its midpoint

How many midpoints can a segment have?

How many segment bisectors can a segment have?

A M B

There are an infinite number of segment bisectors.

H O T

2a + 5 5a - 16

Find a, HO, and OT.

M R P-26 -2

If R is the midpt of MP findMR=_____ RP=_____and the coordinate of R.

R M P-10 18

4x 3x

A B C

6X - 8 2X + 20

Find x and AB, BC and AC.

What are the coordinates of B if C’s coordinate is 70?

-14 -8 -2 0 4 9

W X Y Z T R

Find the possible coordinates of M if YM = 5.

Find the possible coordinates of E on YR if YE = 9

Assignments1st Part of section1.4

Assign pp. 29-31 (1-15 all, 29-35 all)

Part II

Angles

What is an angle? How do you name the following angle?

A

B C

Angle - the union of 2 noncollinear rays whose intersection is a point called the vertex.<ABC or <CBA or

<B

When naming an angle remember…….

The vertex point must always be in the middle

A point from each ray should be on either side of the vertex point

You can name an angle with the vertex pt if it is the only angle at the vertex

Given < ABC Vertex is B Ray BA Ray BC

Can be named <CBA or <B

Classify Angles Acute angles- angles less than 90

degrees Right angles- angles whose

measure = 90 degrees Obtuse angles- angles greater

than 90 degrees Straight angles- angles = 180

degrees (a straight line)

Draw an example of each type of angle.

1.

2.3.

4.

Complementary Angles

2 angles whose sum is 90

12

H

O W

Supplementary Angles

Two angles whose sum is 180.

120 60

H

E Y T A

B

Adjacent Angles

Two angles that have a common ray, a common vertex, and no common

interior points.

12

H

E L

P

Linear PairTwo angles that are

adjacent and supplementary.

A B C

D

1 2

T

A P

E

1 2

Angle Addition Postulate

m < 1 + m < 2 = m <TAP

2x + 8 6 x - 84

Find x and the measure of the 2 angles.

Definition of Linear Pair

2x + 184x

Find x and each angle.

Explain your answer.

Definition of complementary angles.

12 3

A E D

m < 1 = m < 3m < 1 = 10 less than twice m < 2

Find x and the measure of each angle.

m < AOB = 4x + 3, m < BOC = 7X, m < AOD = 16X -1

Solve for x and find the angle measures.

Assignments

2nd part of 1.4Pgs 30-33 (16-19,27-28,70-72,75-78)

2x + 8 6 x - 84

Notebook Quiz

1. Write an equation for the following.

R M P-10 18

4x 3x

2. Write an equation for the following:

Draw a picture to demonstrate each of the

following:

3. Complementary Angles

4. Linear Pair

2x + 8 6 x - 84

Notebook Quiz

1. Write an equation for the following.

R M P-10 18

4x 3x

2. Write an equation for the following:

Draw a picture to demonstrate each of the

following:

3. Complementary Angles

4. Linear Pair