[3rd Grade Math] Let's Master Triangles and Angles!
Hello everyone! Today, let's learn about "triangles" and "angles" together.
If you look around you, you'll find triangles everywhere—in rice balls, clothes hangers, and road signs.
On this page, we'll explain the secrets of triangles and the tricks for identifying their shapes in an easy-to-understand way.
Even if you think, "I'm not very good at geometry," don't worry! We'll take it one step at a time.
What you will learn in this chapter:
・What is an isosceles triangle?
・What is an equilateral triangle?
・All about the size of "angles"
・How to draw triangles using a compass
First, let's start by refreshing our memory on the basics of triangles!
1. Let's get to know two special triangles!
In the 3rd grade, we will learn about two very important types of triangles: the "isosceles triangle" and the "equilateral triangle."
(1) Isosceles triangle
This is a triangle where "two of the sides are the same length."
Take a look at the name! It means a triangle with two equal sides. The name itself is the biggest hint!
【Key Points】
・If two of the three sides are the same length, it is an "isosceles triangle."
・The shape of a house roof or a slender rice ball fits this category.
(2) Equilateral triangle
This is a triangle where "all three sides are the same length."
No matter which side you measure, the length is the same. It's a perfectly balanced, "heroic" shape!
【Key Points】
・If all three sides are the same length, it is an "equilateral triangle."
・Equilateral triangles are also a type of isosceles triangle (because you can say at least two sides are the same length!)
Fun fact: In an equilateral triangle, all the angles are the same size, too.
2. What is an "angle"?
The "corner" part of a triangle is called an "angle."
When two straight lines meet at a single point, the amount of "opening" between them is called the "size of the angle."
【How to identify angle size】
・The length of the lines doesn't matter. You only look at "how wide it is open."
・Imagine a folding fan or an umbrella. The one that is opened wider has the "larger angle."
【Remembering "Right Angles"】
Do you remember the "right angle" we learned about in 2nd grade? It's the shape of that "corner" you get when you fold a piece of origami paper twice.
Some triangles have a right angle, while others have angles smaller or larger than a right angle.
★ Key takeaway:
It is important to look at shapes by paying attention not only to the length of the sides but also to how wide the angles are!
3. Let's try drawing triangles with a compass!
When drawing a triangle with specific side lengths, a "compass" is your best tool.
For example, let's look at the steps to draw an isosceles triangle with sides of \(5cm, 4cm, 4cm\).
1. First, use a ruler to draw a line that is \(5cm\) long. (This is called the base.)
2. Open your compass to a width of \(4cm\).
3. Place the needle on the left end of the line and draw a small arc.
4. Keeping the same width, place the needle on the right end of the line and draw another arc.
5. The point where the two arcs cross like an X (\(\times\)) is your third vertex!
6. Finally, just connect the ends of the base line to the point where the arcs crossed!
【Common mistake】
Sometimes, the width of your compass might slip while you're drawing. The trick is to hold the needle firmly but gently against the paper.
4. Summary and practice advice
Finally, let's summarize the important points we learned today.
・Isosceles triangle: Two sides are the same length.
・Equilateral triangle: All three sides are the same length.
・Angle: The "amount of opening" between two lines.
・Tool: Use a "compass" to accurately transfer lengths.
【A message to all of you doing your best】
At first, it might feel difficult to use a compass, or the names of the triangles might get a bit mixed up. But don't worry!
Start by finding triangles around you and guessing, "Is this an isosceles or an equilateral triangle?"
As you draw triangles by hand over and over, you will naturally become an expert!
Now, open your notebook and try drawing your own perfect equilateral triangle!