Are you ready to be in a love triangle? Sorry, let me rephrase that … are you ready to be in love with a triangle, shape that is? 😉 This triangle printable has a lot to offer and the accompanying refresher has even more. Keep reading to learn how to find the area of a triangle, discover what an isosceles right triangle is, how to find the angle of a triangle, and much more!
When was the last time your child asked you for help with his or her homework, you looked at the problem in question, and drew a complete blank? For me, it’s been a while … but that’s mainly because we’re in the middle of summer! 🙂 I know that the school bus is right around the corner, so I’m getting ready by tidying up my hoard collection of educational printables and reviewing subjects like math.
I created a triangle template printable that can help demonstrate geometry concepts like the perimeter of triangles. As mentioned above, in addition to the free printable triangle shape, this post also includes an all-things-triangle refresher. The refresher will cover:
- What is a triangle shape, including triangle properties (like how many degrees in a triangle) and definitions that answer:
- What is an isosceles triangle?
- What is a scalene triangle?
- What is an equilateral triangle?
- What is an acute triangle?
- What is an obtuse triangle?
- And more!
- Basic triangle geometry including how do you find the area of a triangle and how to find the perimeter of a triangle.
- What the Triangle Inequality Theorem is.
- Much more!
Bonus: Have younger kids and want to help them learn shapes? Head to the Freebie Finding Mom shop to get my 132-page shapes bundle now!
In this 132-page printable shapes worksheets bundle in the Freebie Finding Mom shop you’ll get printable shape tracing worksheets, matching shapes worksheets, shapes coloring pages, counting shapes worksheets, shape pattern worksheets, printable shapes, 2D shapes charts, and shapes flashcards. If you need preschool shapes worksheets or shapes worksheets for kindergarten, you’ll find that and more here! Snag this incredible shapes bundle now!
A lot of the triangle shape refresher information is geared toward school-age children (not your preschooler). However, if you have a little one at home, you can still put this triangle printable to use! Here are some ideas:
- Art project – Drawing, coloring, and crafting are all things that can assist with your kid’s cognitive development and promote creativity. You can use this triangle printable template to help your child learn how to draw a triangle; more on that later … And if you’re looking for something that will also help your child relax (a.k.a. stop bouncing off the walls), definitely consider coloring; snag free printable coloring pages here.
- Matching game – Create a matching game by printing multiples of this triangle printable as well as other shapes, placing them face down, and competing to see who can find the most matching pairs. Not only is this a fun and frugal activity, it will also help your child develop visual memory skills and focus. Here are some other shapes for your game:
- “Driving” game – Create a fake driving or walking course for your kid by using the triangle printable and other shapes to create road signs. For example, with the triangle shape make a yield sign. With the diamond shape make a “slow” sign or traffic light ahead sign. With the octagon shape make a stop sign.
Tip: Your matching game doesn’t need to be limited to shapes. You can use other templates, letters, and numbers to create variations of the game or make it harder as your child learns more. For example, challenge your kid to find the next number in sequential order or to match an uppercase letter to its lowercase match. Download free printable letters and alphabet letters here and browse other bubble letters templates here.
Are those creative juices flowing? Great! Let’s keep moving by talking about what is a triangle and different types of triangles.
A Triangle Definition
Before we can break down the different types of triangles—right triangle, acute triangle, obtuse triangle, congruent triangles—let’s define what a triangle even is. A triangle is a two-dimensional closed polygon that has three straight sides, three angles, and three vertices (points).
How many degrees in a triangle?
All triangles, regardless of the type of triangle, have the same sum of interior angles. The angles of a triangle must add up to 180º. So, if you’re asked how many degrees in a triangle, the answer is always 180º!
What is a right triangle?
A right triangle (or a right angle triangle) is just a type of triangle that has a 90º angle. Keep in mind that a right triangle can only have one 90º angle because the angles of a triangle must add up to 180º and triangles must have 3 angles total.
Not following? If you had a right angle triangle with two 90º angles, that would add up to 180º, but there is still the third angle … and no degrees left. You could not have a third angle that measures 0º. Therefore, a right angle triangle can only have one right angle! 🙂
There are a few special right triangles. They are:
- 3 4 5 triangles (a.k.a. Pythagorean Triple Triangles).
- 30 60 90 triangles.
- 45 45 90 triangles.
More on these special right triangles in just a sec!
What is an isosceles triangle?
An isosceles triangle is a triangle that has two sides of equal length. Do you like a juicy scandal? If so, get ready for a little bit of controversy!
If you read the Free Printable Trapezoid Shape post, you know there are two different ways to define a trapezoid—inclusive and exclusive. The answer to what is an isosceles triangle is similar.
Some people define an isosceles triangle as having only two sides of equal length. Others define them as having at least two sides of equal length, meaning a triangle in which all 3 sides are equal in length would also be considered an isosceles triangle.
There is also an isosceles right triangle (a.k.a. a 45 45 90 triangle) that you should know about. In an isosceles right triangle, the two legs of the triangle are equal in length, which makes their angles congruent (equal), this creates a right angle, which measures 90º.
What is a scalene triangle?
Another type of triangle is the scalene triangle. If you are asked what is a scalene triangle, it’s a triangle where all three sides are different lengths.
You might also be asked what is a right scalene triangle. The right scalene triangle might also be referred to as a “3 4 5 triangle.” More on that in a second. The right scalene triangle is just a scalene triangle (so no equal sides) in which there is a right angle (an angle that measures 90º).
What is an equilateral triangle?
An equilateral triangle is a triangle where all three sides are of equal length and all three angles are of equal measure (60º). So basically it is the opposite of a scalene triangle. 😉
What is an acute triangle?
This is a triangle in which all three angles measure less than 90º. This means there can never be an acute right triangle.
What is an obtuse triangle?
This is a triangle in which one angle of the triangle measures more than 90º. Only one angle in a triangle can be greater than 90º; otherwise, the angles of a triangle would not add up to 180º.
What is a 30 60 90 triangle?
The 30 60 90 triangle is one of the special right triangles. Its angles are always 30º, 60º, and 90º. In addition, the length of the sides always have a consistent relationship to one another. In a 30 60 90 triangle, the ratio is:
- Side opposite the 90º angle: 2 * X
- Side opposite the 30º angle: X
- Side opposite the 60º angle: X * √3
So if you know the value of X (the length of the side opposite the 30º angle), you could easily find the length of the other two sides because the ratio is always the same in this type of triangle.
Tip: The √ means “square root.” If you aren’t familiar with the concept of square root, you can read more here on the square shape post.
What is a 45 45 90 triangle?
The 45 45 90 triangle is another of the special right triangles. It is an isosceles triangle in which two of the angles measure 45º and the other angle is 90º. Recall from the section on isosceles triangles that the two legs are the same length. This means that the length of the two shorter sides of the triangle are equal to one another; the ratio for the length of the long side of the triangle is X * √2.
What is a 3 4 5 triangle?
Also known as a Pythagorean Triple Triangle, this is the last of the special right triangles. It is also a right scalene triangle, which means all three sides are a different length but they have a certain ratio to each other.
The Pythagorean Theorem is written as a² + b² = c². Apply the 3 4 5 triangle to this: 3² + 4² = 5². Is that true? Well, if we solve, it comes out to 9 + 16 = 25, which is in fact true.
If the length of the sides of your triangle can fit that formula, then you are dealing with a 3 4 5 triangle.
What are similar triangles?
When talking about similar triangles, we’re talking about two (or more) separate triangles. The two are said to be “similar triangles” if their corresponding angles are equal to one another and their corresponding sides are proportionately equal. In other words, similar triangles aren’t necessarily the same size, but they are the same proportions, such as two 3 4 5 triangles.
What are congruent triangles
When talking about congruent triangles, we’re talking about two (or more) separate triangles. The two are said to be “congruent triangles” if they are completely equal. This means the length of their corresponding sides are equal as well as the measure of their corresponding angles. In other words, the triangles are a duplicate of one another.
Note: This does not necessarily mean that all three sides or all three angles are the same! You could have congruent scalene triangles.
Download the Printable Triangle Shape
Whew! Who knew there were so many different types of triangle shapes! We haven’t even gotten to the number crunching portion of the post yet. Before we move on, be sure to snag the triangle printable below. It’ll come in handy when explaining various triangle math concepts like the perimeter of triangles.
Bonus: It may be easier to demonstrate some math concepts, like the area of triangle formula with a pre-colored triangle template printable. Where might you find one of those? Oh, right here! 😉 Download the pre-colored free printable triangle shape now.
For younger kids, these printable triangle tracing worksheets may be more their speed.
How to Find the Perimeter of a Triangle
Ready to get at those numbers? If you’re answer is an emphatic “no,” don’t worry; take a deep breath. We’ll start with something simple—the triangle formula for finding perimeter.
Is the word “formula” freaking you out? Yeah, it can sound a little intimidating, but finding the perimeter of triangles is actually pretty easy—all you need is some simple addition.
Before we continue with how to find the perimeter of a triangle or specifically the triangle formula for perimeter, let’s define the word. When it comes to perimeter, all we’re talking about is the measurement around the outside of the shape. So, in this case, all you have to do is add up the measurement of all three sides of the triangle shape.
The triangle formula for finding the perimeter would look something like this:
Perimeter = a + b + c
In that formula, “a,” “b,” and “c” represent the three sides of the triangle.
How to Find the Area of a Triangle
How do you find the area of a triangle? Let’s start by defining area. Whether you’re looking for the area of a right triangle or the area of a home, what you’re looking for is the total space an object is occupying. If you’re looking at the colored triangle printable, the part that is colored in is the area of the triangle shape.
Okay, before we get to the area of triangle formula, let’s be clear … regardless of what type of triangle you’re working with, the area of triangle formula is the same. So the way you find the area of a right triangle, the area of an equilateral triangle, or the area of any triangle is the same.
The area of triangle formula is: Area = (1/2) * b * h
In that formula, “b” stands for the length of the base of your triangle and “h” stands for the height of your triangle. So how to find the area of a triangle calls for you to multiply one-half (1/2) by the length of the base by the height.
Now, while the formula for how do you find the area of a triangle is technically the same, if you are not looking for the area of a right triangle and the height of the triangle is not given to you, it can get a little tricky. For example, if you’re looking for the area of an equilateral triangle you’ll need to find the height of the triangle or use a different formula.
Note: The height is not the length of one of the sides in this case!
So, if you are looking for the area of an equilateral triangle, as long as you know the length of one of the sides, you can still solve the problem even without the height. Here’s the formula you would use: Area = (√3) / 4 * s²
In that formula, “s” stands for the length of one of the sides of the triangle. In order to solve this formula, remember your order of operations!
- Parentheses
- Exponents
- Multiplication or Division
- Addition or Subtraction
So to solve the formula, you would find √3 first, then the square of the length of your side, and then do your division and multiplication.
How to Find the Angle of a Triangle
Finding the angles of a triangle can vary based on what information you’re given and the type of triangle you’re working with. However, one thing will always be the same—the angles must add up to 180º.
So the easiest answer to how to find the angle of a triangle is to already know the measure of two of the angles and to subtract those from 180º. However, depending on the math level your kid is in, the problem may be more complicated. Just remember, at the end, you must have a total of 180º!
What is the Triangle Inequality Theorem
The Triangle Inequality Theorem is actually a pretty simple concept, so I thought it’d be a good note to end on after all that math! A little confidence booster, if you will! 🙂
The Triangle Inequality Theorem states that that the sum of two sides of a triangle must be greater than the third side. So if you think of the sides of a triangle as “a,” “b,” and “c,” then:
- Side a to b + side b to c must be greater than the length of a to c.
- Side a to b + side a to c must be greater than the length of b to c.
- Side b to c + side a to c must be greater than the length of a to b.
If the three sides do not conform to the Triangle Inequality Theorem, the shape cannot actually be a triangle because it couldn’t be a closed shape.
Free Printable 2D Shapes
Had your fill of triangle shapes? No worries, there are plenty more fish in the sea … or should I say shapes in the world? Here are more printable 2D shapes you can download right now!
Download free printable 2D shapes chart in black and white or free printable 2D shapes chart in color.
How to Draw A Triangle
Wondering how to draw a triangle shape? Try one of these two options:
- Decide what kind of triangle you want to draw, break out your ruler, and measure out your lines to ensure they’re straight.
- Snag the printable triangle shape from this post and trace it! (Check out the video in this post for an example; while the video focuses on how to draw bubble letters, the concept is the same for how to draw a triangle.)
Coloring Pages Beyond the Printable Triangle Shape
Not into learning how to draw a triangle shape or other complicated art projects? No worries, rev your creative engine with a coloring sheet. Try the:
Even More Templates
Stay crafty and creative with even more free printable templates!
Letter and Number Printables
Use these letter and number printables to take your matching game up a notch!
- Free printable alphabet calligraphy letters or if it’s more your style a modern calligraphy alphabet.
- Free printable numbers templates including bubble numbers from 0 to 100 and a free printable number stencils set.
