1-5 Angle Relationships What are: adjacent angles linear pairs vertical angles complementary angles...

1-5 Angle Relationships

What are:

adjacent angles

linear pairs

vertical angles

complementary angles supplementary angles

perpendicular lines

Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.

Adjacent angles

12

Linear Pair

A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

1 2

Definition

Two angles, , form a linear pair if and only if A, B, and C are collinear and D is not on .

DBCABD and

AC

A B C

D

Name all the linear pairs

FKGandJKF GKHandFKG

HKJandGKH

F

G

H

K

J

JKFandHKJ

Vertical Angles

OR…When two lines intersect, they form two pairs of vertical angles.

Two angles are vertical angles if and only if their sides form two pairs of opposite rays.

1

2

3

4

Definition

Complementary angles are two angles whose measures add up to 90°

90ABDCBDABC

A

B

C

D

Try itFind the measures of

461m

1

2

3

134°

1342m 463m

.3,2,1

Definition

Supplementary angles are two angles whose measures add up to 180°

180TSURST

R S

T

U

Linear Pair Postulate

The angles in a linear pair are supplementary

What is the difference?

Supplementary because it adds to 180°

Supplementary because it adds to 180°

Linear pair because both angles are on the same line.

AND

Complementary or Supplementary?

Angles can be complementary or supplementary regardless of their location.

PR toarycomplementis

P R

41° 49°41° 139°

P S

PS toarysupplementis

64If Xm find the measures of the angles that are complementary and supplementary to X

Complementary

90°− 64° = 26°

Supplementary

180°− 64° = 116°

Review

p. 46

Review

p. 47

Assignment 1-5

Page 51, 8-17, 19-21

Angle Relationships Day 2

What are perpendicular lines?

What can be assumed or not assumed in a drawing?

Perpendicular Lines

Lines, line segments or rays that form right angles are perpendicular.

A B

CD

Perpendicular Lines A

B

CD

Perpendicular lines intersect to form four right angles.Perpendicular lines intersect to form congruent adjacent angles.Segments and rays can be perpendicular to lines or other line segments and rays.The right angle symbol in the figure indicated that the lines are perpendicular.

To Assume or Not to Assume…

In the figure, do you think you would be justified in assuming that:

B, C, and E are collinear?

?FCEACB BE ll GD?

D

A

BC

E

F

G

Make a List…

Make a list of rules about what you think you can and cannot assume.

A

BC

E

F

G

What can and cannot be assumedYou May Assume: You May Not Assume

(unless marked):Things that look straight are straight. Exact measurements

and relative sizes of figures.

Points shown on a line are collinear.

All points shown are coplanar.

Parallel or perpendicular lines.

Relative position of points are accurate (intersection, between-ness).

Congruence

To Assume or Not to Assume…Point S is between R

and T.Points R,S, and T are

collinear.

Point S is the midpoint of RT.

VY<TY

STRS

ZWVR .anglerightaisZYV

R S TV

W

Y

Z

Assignment 1-5 Day 2

Worksheet 1-5