Download Line and Angle Review Lines, Segments, Rays, and Angles

Line and Angle Review
Thursday, July 11, 2013
10:22 PM
Lines, Segments, Rays, and Angles
Slide
Notes
Title
Lines, Segment, Ray
A line goes on forever, so we use an arrow on each side to
indicate that. You name the line by using two letters on the
line. The are labeled with a letter of the alphabet so that we
can easily talk about the line - it has a name. Other lines
might use different letters. It is all up to the one that draws
it.
A segment is much like a line. It is straight, but instead of
going on forever, it ends at points on the line. Like the line,
Saxon 2_ 3rd ed Page 1
Lines, Segment, Ray
A line goes on forever, so we use an arrow on each side to
indicate that. You name the line by using two letters on the
line. The are labeled with a letter of the alphabet so that we
can easily talk about the line - it has a name. Other lines
might use different letters. It is all up to the one that draws
it.
A segment is much like a line. It is straight, but instead of
going on forever, it ends at points on the line. Like the line,
a segment can be labeled. This time the little symbol above
the letters show a line or can be a line with endpoints.
A ray is a little of both a line and a segment. It ends on one
side but goes on and on forever to the other direction. The
ray symbol is used above its two letter name to show it is a
ray.
Math with Segments
If we write the name of a line in letters without the bar
above them, we are talking about the length of the line.
You can see that here in this problem.
If AC is 13 units and line segment AB is 3 units, how long is
the line segment BC?
Here is how you solve it …
A to C is the total length of the line between the furthest
points that all three points share. The segment AB and BC
will add up to it.
The total of 13 units minus the part of 3 units equals 10
units.
Parallel Lines
Two straight lines in the same plane, such as a piece of
paper or a chalkboard, could intersect or be parallel if you
extend them out forever.
When they never cross, you have parallel lines. These lines
stay at the same distance apart at all times.
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Intersecting Lines
When straight lines cross, you have intersecting lines.
An interesting thing about these is that the angles that are
opposite each other will have the same measure. So the
angles you see here in orange are equal and the angles you
see in white are equal to each other.
Perpendicular Lines
A special type of intersecting line is a perpendicular line.
When these cross, they form ninety degree angles or
square corners.
Right Angles
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Right Angles
Those ninety degree angles or square corners pop up in
squares, rectangles, triangles and just angles by themselves.
Note that 90 degree angles will often be indicated by a
square.
Acute and Obtuse Angles
Angles that are less than 90 degrees can be classified as
acute angles.
When they open up greater than 90 degrees but they are
less than a straight line, they are obtuse.
Straight and Reflex Angles
Straight angles make a straight line. Another way to think of
a straight line is an angle that is opened up 180 degrees.
When an angle is greater than a straight angle but less than
360 degrees, it is a reflex angle.
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Angle Notation
As with the line, segment, and ray, we need a way to name
angles.
When there is just one of them, a simple angle symbol and
a letter is fine to name it.
When there is more than one angle, you start labeling the
ends with letters and use all three to name each angle
combination.
Here is angle TAZ
While here is angle KAZ
When angles share a common vertex, they are called
adjacent angles.
Complementary vs. Supplementary
Angles
When a 90 degree angle is split, we say that the two
adjacent angles are complementary to each other.
When a straight angle is split, the two are supplementary
angles.
The nice thing about these two is that since you know what
they should both add up to, either 180 or 90 degrees, if you
know one of the angles, you can compute the other one.
Protractor
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Protractor
This is a protractor.
It is a useful tool for measuring and creating angles.
Measure and Angle
Let's use the protractor to determine the angle.
Line up the line that marks the center of the ruler at the
bottom with the vertex of the angle. You want the
protractor to follow along one of the sides of the angle.
There are two sets of measurements. The inner one zeros
on the right and the outer one zeros on the left. Assuming
that you want the inner angle select the one that would fall
inside the angle.
Now look where the angle's line crosses the protractor to
get the measurement. This one is 120 degrees.
Create an Angled Ray 1
Sometimes you need to create the angle from scratch. You
don't always even need to draw a two lined angle because
even a ray can have an angle measure. It is almost as if the
invisible horizon line is its other half.
Let's draw a ray that is 40 degrees compared to the horizon
line.
Get as close as you can to making the protractor parallel to
the top and bottom edge of the surface you are drawing on.
Mark the point near the midline and one at the 40 degree
point on the protractor starting from the zero on the right
side.
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Create an Angled Ray 2
Now use the straight edge of the protractor to connect the
two marks to make the ray.
Create an Angled Ray 3
Now you have a 40 degree ray.
Important Angles
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Important Angles
There are certain angles that are more important than
others in mathematics.
O degrees is the point from where you start, but in an angle
that is 360 degrees it wraps all the way back to where it
started.
180 degrees makes a straight angle. Half of that makes 90
degrees. Across from ninety and the midway point between
180 and 360 is the 270 degree angle.
Split the ninety degree angle and you have a 45 degree
angle.
All of these angles pop up over and over again in
mathematics as well as out in the real world.
180 and 360 Degrees
Circles are basically 360 angles.
A semi-circle, or half circle, would be half that, 180 degrees.
Show What You Know
Time now to show what you know.
I am going to call out some angle or line types and you click
on the image that is the best example of it.
Straight angle
Perpendicular lines
Intersecting, but not perpendicular lines
An acute angle
A reflex angle
Obtuse angle
Right angle
Parallel lines
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Parallel lines
Supplementary angles
Complementary angles.
Show What Your Know
Now let's have you take what you know and use it to find
some unknown angles.
What angle in white is shown? Compute it from the angles
you are given and what you have learned about
complement and supplement angles.
Show What You Know
Now try this one.
Think about what you have learned about intersecting lines.
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