Ordering Angles: Lesson for Kids

Instructor: Mark Boster
There is a relationship between the size of an angle and the length of the side opposite it. Knowing this relationship will help you to easily order angles, even when you only have limited information. This lesson will teach you how angle size and side length are related so that you can achieve angle ordering mastery.

Katie and Her Hamster

Katie had a hamster named Bob that she liked to play with. Katie would sit on the ground and let Bob run around in the 'V' her legs would make when she put them out. She had a wood slat she would put between her feet so Bob couldn't escape. She noticed that if she put her feet further apart, she needed larger slats of wood. In other words, when she changed the angle of her legs, the length of the opposite side changed also. Let's investigate this.

Katie's Triangle

If you can, go ahead and sit on the floor. Come on, let's have some fun! Now, put your feet about one foot apart. Now move your feet to about three feet apart. Did you notice that in order to do this, you needed to make a larger angle with your legs? If you did, then you are on the right track to ordering angles! Try it again to make sure that it is true!

Measurements of Angles

When Katie is playing with Bob, let's say the angle of her legs is 30°. But, if she moves her feet apart so the angle is now 45°, would she need a longer or shorter piece of wood to keep Bob in? Let's figure that out. Look at the diagram and see which base is longer. Do you notice how the side across from the 45° angle is longer than the side that is across from the 30° angle? It always works that the vertex, which is the point where two lines meet, with the largest angle is across from the longest base.

As the Angle Gets Larger, the Opposite Side Gets Longer
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Whole Triangles

In the example we just looked at, which used an isosceles triangle, we learned that the larger the angle of the legs, the longer the base. Let's see how that works in other triangles. Look at the red triangle diagram with the angles labeled. If you look, you will see that the longest side of the triangle is across from the 80° angle, which is the largest angle. The second longest side is across from the second largest angle of 52° and the shortest side is across from the 48° angle. And, it always works this way! How cool is that?

Three Angles on a Triangle
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