Geometry notes
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Geometry Notes. Section 1-5 <3 KJMP. What you’ll learn. How to identify and use special pairs of angles Adjacent angles Vertical angles Linear pairs of angles Complementary angles Supplementary angles How to identify perpendicular lines. Vocabulary. Adjacent angles Vertical angles

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Geometry Notes

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Geometry notes

Geometry Notes

Section 1-5

<3 KJMP.


What you ll learn

What you’ll learn. . .

  • How to identify and use special pairs of angles

    • Adjacent angles

    • Vertical angles

    • Linear pairs of angles

    • Complementary angles

    • Supplementary angles

  • How to identify perpendicular lines


Vocabulary

Vocabulary

  • Adjacent angles

  • Vertical angles

  • Linear pair of angles

  • Complementary angles

  • Supplementary angles

  • Perpendicular lines


Adjacent angles

C

C

No Common Vertex

A

A

D

D

Shared Interior

Adjacent Angles

  • Examples: ABC and CBD

B

B

  • Non examples:

CAT and CAS

ABC and  BCD

S

C

D

T

C

B

A

A


Adjacent angles1

Adjacent Angles

  • Adjacent Angles- 2 angles that

    • lie in the same plane

    • have a common vertex

    • have a common side,

    • But have no common interior points (the angles do not overlap).


Vertical angles

Vertical Angles

5

  • Examples:

8

6

1

2

4

7

3

  • NonExamples:

C

B

A

D

E


Vertical angle

Vertical Angle

  • Vertical Angles- 2 nonadjacent angles formed by two intersecting lines.


Linear pair of angles

B

T

C

C

E

R

D

Linear Pair of Angles

Line

  • Example: BED and BEC.

  • NonExample

A


A linear pair of angles

A Linear Pair of Angles

  • A linear pair of angles

    • adjacent angles

    • non-common sides are opposite rays.


Complementary angles supplementary angles

Complementary Angles & Supplementary Angles

  • Complementary: Any pair of angles whose measures add up to 90

  • Supplementary: Any pair of angles whose measures add up to 180


Example problems

Example problems:

  • The measure of an angle’s supplement is 3 times the measure of the angle. Find the angle and its supplement.

  • Two angles are complementary. One angle is 12 more than the other. Find the angle.

  • Find mT if mT is 20 more than 4 times its supplement.


Perpendicular lines

Perpendicular Lines

  • DEFN: Perpendicular lines are lines that intersect to form right angles.

  • Everything you wanted to know about perpendicular lines and more:

    • symbol for perpendicular: 

    • diagram symbol:

    • lines form not just one but, 4 right angles

    • lines form  (congruent)adjacent angles

    • rays and segments can be  too


Have you learned

Have you learned. . .

  • How to identify and use special pairs of angles

    • Adjacent angles?

    • Vertical angles ?

    • Linear pairs of angles?

    • Complementary angles?

    • Supplementary angles?

  • How to identify perpendicular lines?

  • Assignment: Worksheet 1.5


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