Line segments is a part of the line limited by two remote points.
Imagine a line. A line has no beginning and no end.
Now somewhere, anywhere, put a point on it, and chop off one part. Now you got a semi straight line, or a ray.
Now your line is limited on one side, and if you limit it to the other side you get a segment:
We all know what a plane is, a flat endless surface.
An angle is a part of a plane enclosed by two rays. They are measured in degrees (symbol: ᵒ).
= (minutes) = (seconds)
Every angle is made out of three parts vertex and 2 arms (rays).
Angles are divided into six groups based on their measure.
First ones are the smallest – acute angles. Their measure is less than .
Second is the right angle. Right angle is always .
Third is obtuse angle, the one that has more than but less than .
Straight angle is the one whose two arms make a straight line. He always has exactly .
Reflex angle has more than and less than .
Full rotation always has exactly .
Angles can also be measured in radians, where 90 degrees is , 180 degrees , and 360 degrees is .
Converting radians into degrees
We learned that full rotation has or radians. To convert into you have to multiply it by 180 and divide with
By dividing that with two, we get that has radians. If we multiply with and divide it with , we get .
We can generalize that with a formula:
Degrees = radians * . Let’s see how it works.
Convert into degrees.
Converting degrees into radians
Opposite, when converting radians degrees into radians, for example into , you have to divide with and multiply with .
Radians = degrees * .
Convert into radians.
Let’s say you have your side c and points A and B. And you want to construct an angle with measure of in point A.
This angle is enclosed by sides c and b, so you’ll construct your angle in point A. Draw a circle around your point A, it does not matter which radius you chose. Mark intersection of the circle with side c with D. Now draw a circle, with center in D, with the same radius you used to draw previous circle.
Draw a straight line that goes through point A and intersection of two circles you drew. You got a line which contains side b. And you got your angle.
Constructing angle whose measure equals to is very easy since we know how to construct an angle with measure . , and that means that we’ll simply construct two angles of and add them together. Put the needle in your compass in point F-intersection of your circle with previous angle and draw another arc with the same radius.
For constructing an angle with the measure of you’ll have to know how to bisect an angle. Since , we’ll firstly draw angle with . Mark the intersections of arms of an angle and circle with H and C.
We’ll put the needle of a compass in C and make an arc somewhere between H and C and do the same with H, then connect their intersection with our starting point and we got .
Other angles are constructed by combining these. If you want an angle whose measure equals to 15ᵒ you’ll simply bisect angle of 30ᵒ.
If you want 90ᵒ you’ll have to make twice 60ᵒ angle, and bisect the other one to get 30ᵒ and you’ll have 30ᵒ + 60ᵒ = 90ᵒ.
Line segments and angles worksheets
Constructing line segments (173.2 KiB, 164 hits)
Constructing angles (118.4 KiB, 165 hits)
Construction of angle bisectors (438.2 KiB, 148 hits)
Measuring lines in centimeters (105.0 KiB, 290 hits)
Measuring lines in millimeters (73.8 KiB, 238 hits)
Determine a type of angle (238.2 KiB, 150 hits)
Angle relationship (381.1 KiB, 160 hits)
Measure an acute angles (61.1 KiB, 242 hits)
Measure an obtuse angles (57.5 KiB, 252 hits)
Angle measurement (334.9 KiB, 171 hits)
Draw an acute angle (50.6 KiB, 277 hits)
Draw an obtuse angle (78.1 KiB, 216 hits)
Draw different type of angles (251.6 KiB, 161 hits)
Converting degrees into radians (121.2 KiB, 167 hits)
Converting radians into degrees (135.3 KiB, 164 hits)
Coterminal angles (136.9 KiB, 168 hits)