1.5 Angle Relationships. Adjacent Angles Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points.

1.5 Angle Relationships

Adjacent Angles

Two angles that lie in the same plane, have a common vertex and a common side, but no common interior points

Examples: NonExamples:

B is the common Vertex

is the common side

BC

Vertical Angles

Two nonadjacent angles formed by two intersecting linesExamples: NonExamples:

Vertical angles must be formed by a nice neat “X”

Linear Pairs

A pair of adjacent angles whose noncommon sides are opposite rays.

Examples: NonExamples:

ECED & form a straight line

ECED & do not form a straight line

Example 1

Complementary Angles

Two angles whose measures have a sum of 90°

Supplementary AnglesTwo angles whose measures have a sum of 180°

(These angles do not have to be connected)

Example 2

Draw a picture:

What do we know?

90 BAComplementary means a sum of 90°

12 ABDifference means subtract

Solve one equation for one of the variables:

A A

AB 1290 BA

Substitute into the other equation & solve

9012 AA90122 A

722 A36Am ??

,36 If

Bm

Am5436-90 Bm

Perpendicular Lines

Lines that form right angles

Perpendicular lines intersect to form 4 right angles

Perpendicular lines intersect to form congruent adjacent angles

Segments & rays can be perpendicular to lines or to other line segments & rays

The right angle symbol in the figure indicates that the lines are perpendicular

is read as “is perpendicular to”

(Perpendicular lines don’t form 90˚ angles; they form right angles, and right angles have a measure of 90 ˚) – this is a nit-picky fact that will be used in proofs

Example 3

Look for an equation to write & solve.

xx 36 90 1012y 90

xxy 361012 Too many variables; look for something else

909 x

10x10012 y

3.83

25

12

100y Do the solutions

work?

≈ means “approximately equal to” because we rounded the decimal.

If we want the lines to be perpendicular, they have to make right (90˚) angles.

What can you assume?

Make a list of things you “think” might be true

How many did you come up with? Now double check with the chart below. Mark whether each one from your list can be assumed.

Example 4

HW : Page 41 (4– 10 all, 11 – 35 & 39 odds)