Transcript Document

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:
B is the common Vertex
BCis the common side
NonExamples:
Vertical Angles
Two nonadjacent angles formed by two intersecting lines
Examples:
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:
ED & EC
NonExamples:
form a straight line
ED & EC
do not form a straight line
Example 1
Complementary Angles
Two angles whose measures have a sum of 90°
Supplementary Angles
Two 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?
Complementary means a sum of 90°
Difference means subtract
Solve one equation for one of the variables:
A  B  90
B  A  12
A  B  90
A  12  A  90
2A  12  90
If mA  36,
2A  72
mB  ??
mA  36
 A
 A
B  12  A
Substitute into the other equation & solve
mB  90 - 36  54
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.
12y  10  6 x  3x
6 x  3x  90
9 x  90
x  10
Too many variables; look for something
else
12y 10  90
If we want the lines to be perpendicular, they have to
make right (90˚) angles.
12y  100
100 25
y

 8.3
12
3
Do the solutions work?
≈ means “approximately equal to” because we rounded the decimal.
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)