Learn
Download
1 / 22

Learn to understand relationships of angles . - PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on

Learn to understand relationships of angles. Vocabulary. congruent vertical angles adjacent angles complementary angles supplementary angles. Congruent angles have the same measure.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Learn to understand relationships of angles .' - ajaxe


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Learn to understand relationships of angles.


Vocabulary

congruent

vertical angles

adjacent angles

complementary angles

supplementary angles


Congruent angles have the same measure.

Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent.

MRP and NRQ are vertical angles.

MRN and PRQ are vertical angles


MRN and NRQ are adjacent angles. They share vertex R and RN.

NRQ and QRP are adjacent angles. They share vertex R and RQ.

Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.


Additional Example 1A: Identifying Types of Angle Pairs

Identify the type of each angle pair shown.

5 6

5 and 6 are opposite each other and are formed by two intersecting lines.

They are vertical angles.


Additional Example 1B: Identifying Types of Angle Pairs

Identify the type of each angle pair shown.

7 and 8 are side by side and have a common vertex and ray.

7 8

They are adjacent angles.


Check It Out: Example 1A

Identify the type of each angle pair shown.

3 and 4 are side by side and have a common vertex and ray.

3

4

They are adjacent angles.


Check It Out: Example 1B

Identify the type of each angle pair shown.

7

8

7 and 8 are opposite each other and are formed by two intersecting lines.

They are vertical angles.


Complementary angles are two angles whose measures have a sum of 90°.

65° + 25° = 90°

LMN and NMP are complementary.


Supplementary angles are two angles whose measures have a sum of 180°.

65° + 115° = 180°

GHK and KHJ are supplementary.


Additional Example 2A: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are complementary.

The sum of the measures is 90°.

71° + 1 = 90°

1

–71°–71°

m1 = 19°

71°


Additional Example 2B: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are supplementary.

The sum of the measures is 180°.

125° + 2 = 180°

–125°–125°

m2 = 55°

125°

2


Additional Example 2C: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are vertical angles.

3

82°

m3 = 82°

Vertical angles are congruent.


M

L

80°

x

y

J

K

N

Additional Example 2D: Identifying an Unknown Angle Measure

Find each unknown angle measure.

JKL and MKN are congruent.

x + y + 80° = 180°

The sum of the measures is 180°.

–80°–80°

x + y = 100°

Each angle measures half of 100°.

x = 50° and y = 50°


Check It Out: Example 2A

Find each unknown angle measure.

The angles are complementary.

65° + d = 90°

The sum of the measures is 90°.

d

–65°–65°

md = 25°

65°


Check It Out: Example 2B

Find each unknown angle measure.

The angles are supplementary.

145° + s = 180°

The sum of the measures is 180°.

–145°–145°

ms = 35°

145°

s


Check It Out: Example 2C

Find each unknown angle measure.

The angles are vertical angles.

t

Vertical angles are congruent.

mt = 32°

32°


C

D

50°

x

y

A

B

E

Check It Out: Example 2D

Find each unknown angle measure.

ABC andDBE are congruent.

x + y + 50° = 180°

The sum of the measures is 180°.

–50°–50°

x + y = 130°

Each angle measures half of 130°.

x = 65° and y = 65°


Lesson Quiz

1. Identify the type of angle pair shown.

Find each unknown angle measure.

2. The angles are vertical angles.

3. The angles are supplementary.

6

7

adjacent

d

d = 130°

130°

x = 45°

135°

x


Lesson Quiz for Student Response Systems

1. Identify the type of angle pair shown.

A. complementary

B. supplementary

C. adjacent

D. vertical

B

A


Lesson Quiz for Student Response Systems

2. Identify the unknown angle measure if the angles are complementary.

A. 40

B. 50

C. 90

D. 140

A

40


Lesson Quiz for Student Response Systems

3. Identify the unknown angle measure if the angles are supplementary.

A. y =145

B. y =125

C. y =90

D. y =35

A

55


ad