Ch. 1-5: Angle Pairs

Mr. Schaab’s Geometry ClassOur Lady of Providence Jr.-Sr. High School 2015-

2016

Adjacent Angles

Have a common vertex Have a common side, but no common

interior points.

Two coplanar angles

Examples:∡ABC and ∡CBD

AB

D

C

Nonexamples:∡ABC and ∡ABD ∡ABC and ∡BCD

AC

DB

AC

DB

AB

CD

Are they Adjacent or Not???

ADB, BDC

A

B

CD

WVX, YVZ

OKN, MJL

W

X

YZ

V

LM

NO

K

J

Yes

No

No

Vertical Angles

For every set of intersecting lines there are two sets of congruent angles

The two nonadjacent angles formed by two intersecting lines (across the vertex)

Examples: AEB and CED, AED and BEC∡ ∡ ∡ ∡

A B

CED

Are they Vertical or Not???

EFG, GFH

E F

G

H I

J

IHJ, EHJYVZ, WVX

W

X

Y

Z

V

YVZ, ZVW

XVY, WVZ

ZVW, WVX

Complementary Angles Two angles whose measures have a sum of 90 Examples:

1 and 2 are complementary

PQR and XYZ are complementary

12

P

R

Q Y

ZX

50°

40°

Example of Complimentary Angles

60

75

15

?

37

53

Supplementary Angles Two angles whose measures have a sum of 180 Example:

EFH and HFG are supplementary

M and N are supplementary

E F G

H

80°100°N

M

Examples of Supplementary Angles

13545

50130

Linear Pair Is a pair of adjacent angles whose non-common

sides are opposite rays

Common

Side

Noncommon Sides

Are opposite

rays

“stra

ight line”

The angles of a linear pair form a straight line:

Example: ∡BED and ∡BEC

C

B

E

D

Are they a Linear Pair or Not???

EFG, GFH

E F

G

H I

J

IHJ, EHJYXZ, WXZ

YXW, WXZ

EFG, IHJ

W XY

Z

Example 1:Refer to the figure below. Name an angle pair that

satisfies each condition.

a.) two angles that form a linear pair.

∡VZY and YZW∡∡VZX and XZW∡

b.) Name two angles that are acute vertical angles:

∡VZY and XZW∡

(2x + 24)° (4x + 36)°

Example 2: ∡KPL and ∡JPL are a linear pair, m∡KPL = 2x + 24, m∡JPL = 4x + 36. What are the measures of ∡KPL and ∡JPL?

Since ∡KPL and ∡JPL are a linear pair, then we know their sum is 180°m∡KPL + m∡JPL = 180°

(2x + 24) + (4x + 36) = 180°

6x + 60 = 180°

- 60 - 60

6x = 120°

6x = 120°

6 6x = 20°

m∡KPL = 2(20) + 24 = 64°

m∡JPL = 4(20) + 36 = 116°

Check: 116° + 64° = 180°

Angle Bisector A ray that divides an angle into two

congruent angles

Example: If PQ is the angle bisector of

RPS, then RPQ QPS

R Q

SP

Examples 3:

Angle Bisector

A

B

C

D

If mADB = 35,

Y

X

W

Z

If mYZX = 20,

then mBDC = ___then mWZX = ___

then mADC = ___ then mWZY = ___

35

70

2040

Example 4:If BX bisects ABC, find x and mABX and

mCBX.

A X

C

B

3x + 5

2x + 30

Bisector cuts and angle into two equal parts. Then m∡ABX = m∡CBX

m∡ABX = m∡CBX3x + 5 = 2x + 30

-2x -2x

x + 5 = 30- 5 -5

x = 25

m∡ABX = 3(25) + 5 = 80°

m∡CBX = 2(25) + 30 = 80°