Triangle Classification: Identifying an Obtuse Angle from a Geometric Diagram

Triangle Classification with Visual Angle Analysis

Does the diagram show an obtuse 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 an obtuse-angled triangle
00:03 The triangle has a right angle, therefore it's a right triangle and not obtuse
00:06 This is the solution

Step-by-step written solution

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1

Understand the problem

Does the diagram show an obtuse triangle?

2

Step-by-step solution

To find out whether the depicted triangle is obtuse, let's recall the definition: an obtuse triangle has one angle that measures more than 9090^\circ.

In the diagram provided, we can see a triangle formed by lines drawn from the corners of what visually exists as a right angle, delineated by perpendicular segments. The prominent line bisecting these seemingly perpendicular segments does not suggest any expansion beyond each vertical or horizontal alignment inherent in the right angle setup.

Nevertheless, observe the vertex that connects these aligned angles: their linear combination and spatial property depiction give no notice of expansion over 9090^\circ.

Analyzing the configuration directly or using the properties of straight lines and angle calculations yields no evidence for an angle exceeding 9090^\circ. Therefore, the angles shown collectively correspond to a right triangle, indirectly confirmed via its geometric balance among straight, equal line segments.

Therefore, the diagram does not illustrate any feature of an obtuse triangle.

Consequently, the answer to the question "Does the diagram show an obtuse triangle?" is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Definition: Obtuse triangles have one angle greater than 9090^\circ
  • Technique: Check each vertex for angles exceeding 9090^\circ using visual cues
  • Check: Right triangles have exactly one 9090^\circ angle, no obtuse angles ✓

Common Mistakes

Avoid these frequent errors
  • Confusing right triangles with obtuse triangles
    Don't assume any triangle with a square corner symbol is obtuse = wrong classification! The square symbol indicates a 9090^\circ angle, not an obtuse angle. Always remember that obtuse angles must be greater than 9090^\circ, while right angles are exactly 9090^\circ.

Practice Quiz

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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 at it?

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An obtuse angle looks "wider" than a right angle - it opens up more than a square corner. If you see a small square symbol at a vertex, that's exactly 9090^\circ, not obtuse!

Can a triangle have more than one obtuse angle?

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No! A triangle can have at most one obtuse angle. If two angles were obtuse (each > 9090^\circ), their sum alone would exceed 180180^\circ, which is impossible since all three angles must sum to exactly 180180^\circ.

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

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Acute triangles: All angles < 9090^\circ
Right triangles: Exactly one angle = 9090^\circ
Obtuse triangles: Exactly one angle > 9090^\circ

Why does this triangle look like it might be obtuse?

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The diagram might be confusing because of perspective or drawing style, but look for the right angle symbol (small square). This indicates a 9090^\circ angle exactly, making it a right triangle, not obtuse.

How do I identify triangle types in real problems?

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Look for these clues: Square symbols = right triangle, wide-looking angles = possibly obtuse, sharp-looking angles = possibly acute. When in doubt, measure or calculate the angles if possible!

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