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Geometry Notes. Lesson 1.3A – Angles LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics and complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines. Angle.

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geometry notes

Geometry Notes

Lesson 1.3A – Angles

LG.1.G.4

Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics and complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines.

angle
Angle
  • The figure formed by two rays with a common endpoint.

side

vertex

side

three ways to name an angle
Three ways to name an angle:
  • The vertex (only when there is one angle at the vertex)
  • Three letters (vertex is always the middle letter)
  • A number
angle addition postulate

A

B

D

C

Angle Addition Postulate
  • If D is in the interior of ABC, then m ABD + m DBC = m ABC
example

A

B

D

C

Example…

Given m ABD = 45°

m DBC = 32°

m ABC = _____________

now you try

S

R

25°

50°

T

43°

Q

P

Now You Try…
  • m SQT = _________
  • m PQR = _________
  • m SQP = _________
types of angles

X

Y

O

Z

W

Types of Angles
  • Vertical Angles – nonadjacent angles formed by two intersecting lines
  • Name a pair of vertical angles.
  • Look at the size (measurement) of one pair of vertical angles. What might you guess about their measurements?
now you try1

A

C

E

O

D

F

B

Now You Try…

Name a second angle in each pair of vertical angles.

  • EOD
  • BOC
  • EOB
types of angles cont

D

105O

75O

C

Types of Angles (cont.)
  • Supplementary Angles – two angles, whose sum of their measures equals180°

Angles C and D are supplementary.

example1

xo

120o

Example…

x =

types of angles cont1

50O

A

40o

B

Types of Angles (cont.)
  • Complementary Angles – two angles, whose sum of their measures equals 90°

Angles A and B are complementary.

example3

K

L

P

M

N

Example . . .

Given: KLM is a right angle.

  • If m KLP = 57°, find m MLP.
  • If m MLP = 69°, find m KLP.
  • If m NPM = 120°, find m MPL.
  • If m KPL = 130°, find m KPN
now you try2

B

C

E

D

A

Now you try. . .

Given: BAD is a right angle.

  • If m BAE = 74°, find m EAD.
  • If m EAD = 36°, find m BAE.
  • If m CED = 71°, find m CEB.
  • If m AED = 117°, find m BEA.