Do Now Draw each figure. 1. line segment 2. line 3. ray 4. plane

Do NowDraw each figure.

1. line segment

2. line

3. ray

4. plane

Course 2

8-3EQ: How do I identify parallel, perpendicular, and angles formed by a transversal?

HWK: Wbk P 70

• M7A2a Given a problem, define a variable, write an equation, solve the equation and interpret the solution.

Vocabulary ReviewAngle – Vertex - right angle - angle that that measures.

The symbol Γ indicates a right angle.

Insert Lesson Title Here

Course 2

Angles

acute angle - is an angle that measures

obtuse angle - an angle that measures

straight angle - is an angle that measures

complementary angles – the sum of the measures of two angles is ?0

supplementary angles – the sum of the measures of two angles is ?°

New Vocabulary

perpendicular lines - angles formed by two

intersecting lines are equal to 90°

parallel lines - lines in the same plane do

not intersect at all

adjacent angles – angles that have a

common vertex and a common side, but

no common interior points.

vertical angles - opposite angles formed

by two intersecting lines

Transversal - a line that intersects two or

more lines

corresponding angles - are angles on the

same side of the transversal and are

both above or both below the parallel

lines

An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.

Angles are measured in degrees (°).

A

CB

1

Vertex

Course 2

8-3 Angles

An angle’s measure determines the type of angle it is.

A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.

An obtuse angle is an anglethat measures more than 90°but less than180°.

A straight angle is an anglethat measures 180°.

Course 2

8-3 Angles

Tell whether each angle is acute, right, obtuse or straight.

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

Course 2

8-3 Angles

Check It Out: Example 1


Tell whether each angle is acute, right, obtuse, or straight.

A. B.

straight angle acute angle

Course 2

8-3 Angles

Course 2

8-3 Angles

You can name this angle ABC, CBA, B, or 1.

Reading Math

A •

B • • C

1

If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.

Course 2

8-3 Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Course 2

8-3 Angles

OMP and PMQ

complementary.

O

N

P Q

R

M

Course 2

8-3 Angles

If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°.

Reading Math


Course 2

8-3 Angles

NMO and OMR

O

N

P Q

R

M


Course 2

8-3 Angles

PMQ and QMR

O

N

P Q

R

M


Course 2

8-3 Angles

BAC and CAF

C

B

D

E

F

A


Course 2

8-3 Angles

CAD and EAF

C

B

D

E

F

A


Course 2

8-3 Angles

BAC and EAF

C

B

D

E

F

A

Angles A and B are complementary. If mA is 56°, what is the mB? What is the supplement of A?

Course 2

8-3 Angles

Angles P and Q are supplementary. If mP is 32°, what is the mQ? What is the complement of P?

Course 2

8-3 Angles

The symbol means “is parallel to.” The symbol means “is perpendicular to.”

Reading Math

Course 2

8-3 Angle Relationships

Tell whether the lines appear parallel or perpendicular.

The lines appear to intersect to form right angles.

UV and YV

UV YV

Course 2



The lines are in the same plane and do not intersect.

XY and WZ

XY || WZ

Course 2



The lines appear to intersect to form right angles.

WX and XU

WX XU

Course 2



The lines are in the same plane and do not intersect.

WX and ZY

WX || ZY

Course 2


Course 2


Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.

Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

Course 2


A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.

Course 2


Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.

Line n line p. Find the measure of the angles.

Course 2


Line n line p. Find the measure of the angles.

45°

2 3 135°

5 647

n p

Course 2


Tell whether each angle is acute, right, obtuse, or straight.


1. straight

obtuse

Course 2

8-3 Angles TOTD

2.



3. AZB and BZC neither

Course 2

8-3 Angles TOTD

4. BZC and CZD complementary

5. Angles M and N are supplementary. If M is 117°, what is mN? 63°

Tell whether the lines appear parallel, perpendicular, or skew.

1. AB and CD

2. EF and FH

perpendicular

parallel


Course 2

8-3 Angle Relationships TOTD

Do Now Draw each figure. 1. line segment 2. line 3. ray 4. plane

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