Geometric Analysis: Determining if a Triangle is Obtuse Using Visual Properties

Q: How can I tell if an angle is obtuse just by looking?

An obtuse angle looks wider than a square corner. Imagine the corner of a piece of paper - if any angle in the triangle opens wider than that, it's obtuse!

Q: What if the triangle looks almost like it has an obtuse angle?

When in doubt, compare to a right angle reference. If you're not sure, the angle is probably not obtuse - obtuse angles should be clearly wider than $90^\circ$.

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

No! A triangle can have at most one obtuse angle. If it had two obtuse angles, the angles would add up to more than $180^\circ$, which is impossible.

Q: Does the triangle's shape tell me if it's obtuse?

Yes! Obtuse triangles typically look stretched or flattened in one direction, with one very wide angle. Equilateral triangles (like this one appears to be) have all angles equal to $60^\circ$.

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

Acute: All angles less than $90^\circ$Right: One angle exactly $90^\circ$Obtuse: One angle greater than $90^\circ$

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is an obtuse triangle

00:04 Draw the perpendicular to the angle

00:09 We can observe that this angle is less than 90 degrees

00:20 Apply the same method for the remaining angles

00:29 This angle is also less than 90 degrees

00:40 This angle is also less than 90 degrees, therefore the triangle is an acute triangle

00:50 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Does the diagram show an obtuse triangle?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Understand the definition of an obtuse triangle.
Step 2: Analyze the visual representation of the triangle in the diagram.
Step 3: Conclude if the triangle has an angle greater than $90^\circ$ .

Now, let's work through each step:
Step 1: An obtuse triangle has one angle measuring more than $90^\circ$ .
Step 2: Upon observing the given diagram, the triangle appears symmetric and evenly proportioned. Typically, such geometries suggest all angles are less than or equal to $60^\circ$ .

The triangle visually does not show characteristically obtuse features like a visibly extended angle, as labeled or perceptible in the typical triangular arrangement.
Step 3: Based on our observations and deductive examination of the portrayed triangle, it seems unlikely that any angle within it exceeds $90^\circ$ .

Therefore, the solution to the problem is No, the diagram does not show an obtuse triangle .

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic

Definition: Obtuse triangles have one angle greater than $90^\circ$
Visual Analysis: Look for wide, stretched angles that appear larger than square corners
Verification: Check if triangle appears symmetric with balanced proportions ✓

Common Mistakes

Avoid these frequent errors

Assuming all triangles with wide bases are obtuse
Don't assume a triangle is obtuse just because it looks flat or has a long base = wrong classification! The base length doesn't determine angle size. Always examine the actual angle openings, especially looking for any angle that appears wider than a right angle corner.

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 obtuse just by looking?

+

An obtuse angle looks wider than a square corner. Imagine the corner of a piece of paper - if any angle in the triangle opens wider than that, it's obtuse!

What if the triangle looks almost like it has an obtuse angle?

+

When in doubt, compare to a right angle reference. If you're not sure, the angle is probably not obtuse - obtuse angles should be clearly wider than $90^\circ$ .

Can a triangle have more than one obtuse angle?

+

No! A triangle can have at most one obtuse angle. If it had two obtuse angles, the angles would add up to more than $180^\circ$ , which is impossible.

Does the triangle's shape tell me if it's obtuse?

+

Yes! Obtuse triangles typically look stretched or flattened in one direction, with one very wide angle. Equilateral triangles (like this one appears to be) have all angles equal to $60^\circ$ .

What's the difference between acute, right, and obtuse triangles?

+

Acute: All angles less than $90^\circ$
Right: One angle exactly $90^\circ$
Obtuse: One angle greater than $90^\circ$

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Geometric Analysis: Determining if a Triangle is Obtuse Using Visual Properties

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