Triangle Side Analysis: Determining if ABC is an Equilateral Triangle

Q: How do I know if X+X is the same as 2X?

Yes! X+X = 2X by the distributive property. Think of it like having 1 apple + 1 apple = 2 apples. Similarly, one X plus one X equals two X's.

Q: Can X be negative or zero?

For a real triangle, X must be positive since side lengths are always positive. If X≤0, then $2X \leq 0$, which isn't a valid side length.

Q: What's the difference between equilateral, isosceles, and scalene?

Equilateral: All 3 sides equal (like this triangle)Isosceles: Exactly 2 sides equalScalene: All 3 sides different lengths

Q: Do I need to find the actual value of X?

No! Since all three sides are 2X, they're equal for any positive value of X. You don't need to solve for X to determine the triangle type.

Triangle Classification with Algebraic Side Lengths

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is equilateral

00:02 Calculate the side lengths according to the given data

00:05 All sides are equal, therefore the triangle is equilateral

00:08 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the size of the 3 sides of the triangle, is it an equilateral triangle?

Step-by-step solution

To determine whether the triangle is equilateral, follow these steps:

Simplify each side of the triangle, labelled as "X+X", to express it as $2X$ .
Check the lengths of the sides:

The first side is $2X$ .
The second side is also $2X$ .
The third side is again $2X$ .

Since all three sides have the same length of $2X$ , the triangle is equilateral.

Therefore, the conclusion is that the triangle is indeed equilateral.

The solution corresponds to choice 2.

Yes

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Equilateral triangles have all three sides of equal length
Simplification: X+X = 2X, so all three sides equal 2X
Verification: Compare all side lengths: 2X = 2X = 2X ✓

Common Mistakes

Avoid these frequent errors

Not simplifying algebraic expressions first
Don't compare X+X directly with 2X = different-looking expressions seem unequal! Students think the sides are different lengths. Always simplify algebraic expressions like X+X to 2X before comparing side lengths.

Practice Quiz

Test your knowledge with interactive questions

Is the triangle in the drawing a right triangle?

FAQ

Everything you need to know about this question

How do I know if X+X is the same as 2X?

Yes! X+X = 2X by the distributive property. Think of it like having 1 apple + 1 apple = 2 apples. Similarly, one X plus one X equals two X's.

What if X has a specific value, like X=5?

The triangle is still equilateral! If X=5, then each side is 2X = 2(5) = 10. All three sides equal 10, so it's equilateral regardless of X's value.

Can X be negative or zero?

For a real triangle, X must be positive since side lengths are always positive. If X≤0, then $2X \leq 0$ , which isn't a valid side length.

What's the difference between equilateral, isosceles, and scalene?

Equilateral: All 3 sides equal (like this triangle)
Isosceles: Exactly 2 sides equal
Scalene: All 3 sides different lengths

Do I need to find the actual value of X?

No! Since all three sides are 2X, they're equal for any positive value of X. You don't need to solve for X to determine the triangle type.

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