There are some rules that triangles follow that you will need to be familiar with in order to answer all of the questions on the GED math test correctly.
Angles Add up to 180°
The three angles of a triangle have to equal 180 when added together. Knowing this can come in handy when you are asked the measure of one of the angles and the question provides the measures of the other two angles.
Let’s say you were shown the above image on the test and asked to provide the measure of ∠A. First add up the measure of the two angles provided:
95 + 55 = 150
Then subtract that from 180 to find the measure of the missing angle:
180 – 150 = 30
m ∠A = 30°
When All Sides are Equal, All Angles are Equal
You could provide the measure of a missing angle even if you are provided the measure of only one of the other other angles. This is because when you know all sides are equal, then all angles are also equal to each other.
If you were given the above triangle and asked for the measure of ∠A you don’t need to know the measure of ∠B as we did on the first example of this page. This is because we can see that all sides are equal (all are 10 feet). Therefore we know that all angles are also equal, and since we see that one angle is 60° we know that the other two angles are also 60°.
The same goes for the lines of the side.
If you were asked the length of line AB or line BC you would know, because of the same rule above, that it is 10 feet.
Every Triangle’s Formula for Area is A = ½ x base x height
This makes sense when you remember that a rectangle’s formula for area is length x width, and a triangle is basically half of a rectangle (the base of the triangle equaling the length of the rectangle). This formula can be used in situations that might not seem obvious at first. Check the video below for an example.
The Pythagorean Theorem
a² + b² = c²
The Pythagorean Theorem is very useful at finding the missing length of a side of a triangle. It only works for right triangles (triangles that have a 90° angle) however. The a and b in the formula are the two legs of the triangle (those that come together to form the right angle). The c is the longest side, the hypotenuse.
a² + b² = c² can be used to find the length of a missing leg or the length of the hypotenuse. The formula is originally set up to find the length of the hypotenuse.
a² + b² = c²
5² + 12² =c²
First square a and b:
25 + 144 = c²
Add them together:
169 = c²
Now to find c, you need to get c alone, which means getting rid of the ². The way to get rid of ² is to find the square root (√), which means you need to find the square root of the other side.
√169 = c
If you don’t know the square root of 169 in your head, you can guess and check. You just saw that 12 squared is 144, so that’s close. Try 13 x 13.
c = 13 miles.
Now let’s say a question on the test requires you to find the length of one of the legs.
The first thing you need to do is rearrange the formula (a² + b² = c²) to get the missing variable (in this case, b) by itself on one side of the equation.
If you are trying to find the length of a side of triangle or the measure of an area you can use another triangle that you know more about, even if the triangle is bigger or smaller than the one you are trying to find out about. However, both triangles need to have equal angle measurements.
For example, lets say you want to find the height of a cell phone tower. It’s too high to measure, but you can use a basketball hoop, which you know is 10 feet high to calculate the height of the tower based on the shadows both objects cast.
Since you can measure the length of both shadows and you know that both triangles are right triangles (have a 90° angle) and you know the height of the basketball hoop, you can use the things you know to find what you don’t know, the height of the tower.
Put the two sides of the triangle you know in one fraction, for example:
The ten of the hoop height over the fifteen of the basketball length. Now the two sides of the triangle you only partially know go in another fraction, using an x to stand for what you don’t know:
It doesn’t matter what goes on top and what goes on bottom, just keep it the same for both fractions. In our example the heights are both on the top and the shadow lengths are both on the bottom. Now you cross multiply and solve for x:
The height of the cell phone tower is 133 and a third feet.