Transcript (a Right Angle), and

Warm-Up
Judging by appearances, will the lines intersect?
1.
2.
Name the plane represented by each surface of the box.
3. the bottom
4.
the top
5. the front
Angles
• Objective 2.02 Apply properties,
definitions and theorems of angles and
lines to solve problems
We can specify an angle by using a point on each ray and the vertex.
The angle below may be specified as angle ABC or as angle CBA;
you may also see this written as <ABC or as <CBA.
Note how the vertex point is always given in the middle.
Name the angle below in four ways.
The name can be the number between the sides of the angle:
The name can be the vertex of the angle: <G.
Finally, the name can be a point on one side, the vertex, and a
point on the other side of the angle: <AGC, <CGA.
3
4 Types of Angles
Acute Angles
An acute angle is an angle measuring
between 0 and 90 degrees.
Example:
The following angles are all acute angles.
Obtuse Angles
An obtuse angle is an angle
measuring between 90 and 180
degrees.
Example:
The following angles are all
obtuse.
4 Types of Angles Con’t
Right Angles
A right angle is an angle measuring 90
degrees.
Two lines or line segments that meet at a
right angle
are said to be perpendicular.
Note that any two right angles are
supplementary angles
(a right angle is its own angle supplement).
Example:
The following angles are both right angles.
Straight Angle
A straight angle is 180 degrees
A straight angle changes the direction
to point
the opposite way.
Sometimes people say “
You did a complete 180 on that!" ...
meaning you completely changed
your mind, idea or direction.
All the angles below are straight
angles:
Name all pairs of angles in the diagram that are:
a. vertical
Vertical angles are two angles whose sides are opposite rays.
Because all the angles shown are formed by two intersecting lines,
1 and 3 are vertical angles, and 2 and 4 are vertical angles.
b. supplementary
Two angles are supplementary if the sum of their measures is 180.
A straight angle has measure 180,
and each pair of adjacent angles in the diagram forms a straight angle.
So these pairs of angles are supplementary:
1 and 2,
2 and 3 , 3 and 4, and 4 and 1.
Use the diagram below.
Which of the following can you conclude: 3 is a right angle,
1 and 5 are adjacent,
3 is congruent to 5?
You can conclude that 1 and 5 are
adjacent
because they share a common side, a
common
vertex, and no common interior points.
3 and 5 are not marked as congruent on the diagram. Although
they are opposite each other, they are not vertical angles. So you
cannot conclude that 3 5.
3 is not marked as a right angle, so you cannot conclude
that it is a right angle
Find the value of x.
The angles with labeled measures are vertical angles because their
sides are opposite rays. Apply the Vertical Angles Theorem to find x.
4x – 101 =2x + 3
Supplementary Angles
Two Angles are Supplementary if they add up to 180 degrees
These two angles (140° and 40°) are
Supplementary Angles,
because they add up to 180°.
But the angles don't have to be together.
These two are supplementary because
60° + 120° = 180°
Complementary Angles
Two Angles are Complementary if they add up to 90 degrees (a Right Angle).
These two angles (40° and 50°) are Complementary Angles,
because they add up to 90°.
But the angles don't have to be together.
These two are complementary because 27° + 63° = 90°
How can you remember which is which? Easy! Think:
•"C" of Complementary stands for "Corner"
(a Right Angle), and
•"S" of Supplementary stands for "Straight" (180 degrees is a straight line)
On Your Own
m
LNV = _________
m
LNB = 31
m LJC = _________
m GJC = 77
Homework: What Do You Call
It When 50 People Stand on a
Wooden Deck?