# Triangles for SAT Prep

by

**Table Of Contents**

## What is a triangle?

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**Figure #1**

**Figure #2**

Now that we have discussed some properties of a triangle, let’s apply what we know to some examples.

## Examples

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**Find the area of each given triangle.**

#1

**Remember:**

The area of a triangle is .

The base, , can be any side of the triangle. The height, , is a line perpendicular to the chosen base. In **Figure #3**, we can see that we already have a line perpendicular to one of the sides of the triangle. So, the side that measures 20 will be our base. The line that is perpendicular to our chosen base will be our height, which measures 5.

So, &

Now all we must do is plug each value into our area formula and solve.

The area of this triangle is **50 square units**.

**Side Note:**

The side with the measure of 10 **IS** **NOT** the height. It is possible for it to be a base for us to select, but we would also need a line to be perpendicular to the given side. Since there is no line perpendicular to this side, we can’t use it as our base.

#2

In **Figure #4**, the base is 100 and the line perpendicular to the base measures 24.

So, &

The area of this triangle is **1200 square units**.

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**Find the missing angle, ****, of each given triangle.**

#3

**Remember:**

The sum of the interior angles of a triangle **MUST** equal

To find* ** ***Figure #5**, we can make the following equation:

Simplifying, we get

Next, we can isolate by subtracting from both sides.

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#4

For **Figure #6**, we need to create an equation to solve for . Since the sum of the interior angles is , we can write:

Which can be rewritten as

Simplifying, we get

Subtracting from both sides we get

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