Triangle Classification: Determining if a Triangle is Acute-Angled

Q: How can I tell if an angle is exactly 90 degrees?

Look for the small square symbol in the corner! This universal mathematical symbol always indicates a right angle (exactly 90°). You can also check if two lines are perpendicular.

Q: What's the difference between acute and right triangles?

Acute triangles have all angles less than 90°, while right triangles have exactly one 90° angle. A triangle cannot be both acute and right at the same time!

Q: Can a triangle have more than one right angle?

No! The sum of all angles in any triangle is always 180°. If you had two 90° angles, that's already 180°, leaving 0° for the third angle - which is impossible.

Q: How do I identify an obtuse triangle?

An obtuse triangle has exactly one angle greater than 90°. If you see an angle that looks 'wide' or 'open', it might be obtuse. Look for angles between 90° and 180°.

Q: Do I need to measure all three angles?

Not always! If you find one angle that's 90° or greater, you immediately know the triangle is not acute. Only if all visible angles appear less than 90° do you need to check further.

Triangle Classification with Angle Measurement

Is the triangle in the drawing an acute-angled 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 acute-angled

00:03 The triangle has a right angle, therefore it is a right triangle

00:06 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Is the triangle in the drawing an acute-angled triangle?

Step-by-step solution

To determine if the triangle in the drawing is acute, we must evaluate the angles formed by its lines:

The illustration consists of a triangle with a right angle formed between a vertical and a horizontal line.
By definition, an acute-angled triangle is one where all three interior angles are less than 90 degrees.
However, a right triangle has one angle precisely equal to 90 degrees.

In this case, the triangle is a right triangle formed by perpendicular lines (vertical and horizontal lines meet at a right angle). Thus, this triangle contains a 90-degree angle.

Because one of the angles is exactly 90 degrees, the triangle is not an acute-angled triangle.

Therefore, the correct conclusion is that the triangle in the drawing is not acute.

No, the triangle in the drawing is not an acute-angled triangle.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Acute Definition: All three angles must be less than 90 degrees
Right Angle Recognition: Square symbol indicates exactly 90 degrees in corner
Verification: If any angle equals or exceeds 90°, triangle is not acute ✓

Common Mistakes

Avoid these frequent errors

Confusing right triangles with acute triangles
Don't assume a triangle is acute just because it looks 'sharp' = wrong classification! A right triangle has exactly one 90° angle, making it impossible to be acute. Always check if any angle equals 90° using the square corner symbol.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

How can I tell if an angle is exactly 90 degrees?

Look for the small square symbol in the corner! This universal mathematical symbol always indicates a right angle (exactly 90°). You can also check if two lines are perpendicular.

What's the difference between acute and right triangles?

Acute triangles have all angles less than 90°, while right triangles have exactly one 90° angle. A triangle cannot be both acute and right at the same time!

Can a triangle have more than one right angle?

No! The sum of all angles in any triangle is always 180°. If you had two 90° angles, that's already 180°, leaving 0° for the third angle - which is impossible.

How do I identify an obtuse triangle?

An obtuse triangle has exactly one angle greater than 90°. If you see an angle that looks 'wide' or 'open', it might be obtuse. Look for angles between 90° and 180°.

Do I need to measure all three angles?

Not always! If you find one angle that's 90° or greater, you immediately know the triangle is not acute. Only if all visible angles appear less than 90° do you need to check further.

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