Identifying Right Triangles: A Simple Guide

• A. Acute
• B. Right
• C. Obtuse
• D. Scalene

Answer: (B)

Identifying Right Triangles: A Simple Guide

Are you gearing up for the Ontario Mathematics Proficiency Test? Well, you’re in the right place! Today we’ll walk through how to identify one type of triangle that often pops up in such assessments: the right triangle. You know, the ones that come with a neat little rule called the Pythagorean theorem.

What’s the Big Deal About Right Triangles?

First off, let’s get on the same page about what a right triangle is. A right triangle features one angle that’s exactly 90 degrees. Imagine the perfect corner of your room or the step on a staircase – that’s the hallmark of right angles. But what’s the catch? You’ll usually need to figure out whether a triangle with specific side lengths falls into this category.

Meet the Pythagorean Theorem

The Pythagorean theorem is practically the superhero of triangle classification. If you’ve forgotten, it states that in a right triangle, the square of the length of the hypotenuse—that’s the longest side—equals the sum of the squares of the other two sides. Symbolically, it looks like this:

[ c^2 = a^2 + b^2 ]

In our triangle with sides measuring 5 cm, 12 cm, and 13 cm, we need to determine which of these sides is the hypotenuse. Spoiler alert: it’s 13 cm.

Time to Do Some Math!

Let’s crunch some numbers together:

1. First, calculate the squares of the two shorter sides:

• For the side measuring 5 cm:

[ 5^2 = 25 ]

• For the side measuring 12 cm:

[ 12^2 = 144 ]

2. Now, let’s sum those squares together:

[ 25 + 144 = 169 ]

3. Finally, we check the square of our longest side:

[ 13^2 = 169 ]

Ta-da! Since both sides equal 169, we’ve just verified that our triangle is indeed a right triangle. Feels good, right?

Understanding Triangle Classifications

Beyond right triangles, do you know about other types? Here’s a quick rundown:

• Acute Triangle: All three angles are less than 90 degrees. Think of a cute little pie slice.

• Obtuse Triangle: One angle is greater than 90 degrees, like a reclined chair.

• Scalene Triangle: All sides and angles are different—uniqueness is the name of the game here!

Understanding these distinctions not only helps you ace your tests but also makes geometry feel a bit like a puzzle waiting to be solved.

Wrap Up—What's Next?

So, what’s the takeaway? Knowing how to use the Pythagorean theorem makes identifying right triangles a breeze. Plus, this skill will certainly come in handy if you encounter questions about triangle classification in your upcoming assessments.

Keep practicing, and soon you’ll find that you can spot these triangles like a seasoned math maestro. Stay curious and keep building those math skills! Who knows, the world of geometry might just surprise you with its wonders.