Download 9.1 Points, Lines, Planes, and Angles

9.1 Points, Lines, Planes, and
Angles
Part 2: Angles
Parts of an Angle
• An angle is made up of two rays with a common
endpoint.
– The rays forming the angle are
called its sides.
– The common endpoint of the rays
is the vertex of the angle.
– The angle is formed by points on the rays and NO
OTHER points. (Point X is NOT a point on the
angle; it is in the interior of the angle.)
• This angle can be named B, ABC, or CBA.
– The textbook uses the symbol  for “angle”.
Types of Angles
• A tool called a protractor can be used to measure
angles.
• You can classify angles according to their measures.
Symbol for right angle!
Other Types of Angles
• When two lines intersect to form right angles,
they are called perpendicular lines.
– Our sense of vertical and horizontal
depends of perpendicularity.
• When two lines intersect, they form two
pairs of vertical angles.
– Vertical angles always have equal
measures.
Finding Angle Measures
• Find the measure of each marked angle in the
given figure.
Find the measure of each marked
angle in the given figure.
Find the measure of each marked
angle in the figure, given that ABC is
a right angle.
Complementary and Supplementary
Angles
• If the sum of the measures of two angles is 90,
the angles are said to be complementary, and
each is called the complement of the other.
• If two angles have a sum of 180, they are
supplementary, and each is the supplement of
the other.
• If a represents the degree measure of an angle,
90 – a represents the measure of its complement
and 180 – a represents the measure of its
supplement.
Using Complementary and
Supplementary Angles
• The supplement of an angle measures 10
more than three times its complement. Find
the measure of the angle.
The supplement of an angle
measures 25 more than twice its
complement. Find the measure of the
angle.
Angle Relationships
1 2
• A transversal is a line that intersects two
3 4
parallel lines (line t).
• Two angles are corresponding angles if they
5 6
occupy corresponding positions (1 and 5,
7 8
3 and 7, 2 and 6, 4 and 8).
t
– These angles are equal.
• Two angles are alternate exterior angles if they lie outside the two
lines on opposite sides of the transversal (1 and 8, 2 and 7).
– These angles are equal.
• Two angles are alternate interior angles if they lie between the two
lines on opposite sides of the transversal (3 and 6, 4 and 5).
– These angles are equal.
• Two angles are same side interior angles if they lie between the two
lines on the same side of the transversal (3 and 5, 4 and 6).
– These angles are supplementary.
Finding Angle Measures
• Find the measure of each marked angle, given
that lines m and n are parallel.
Assume that lines m and n are
parallel. Find the measure of each
marked angle.