Geometric Analysis: Identifying Acute Triangles from Visual Data

Q: How can I tell if an angle is less than 90° just by looking?

Compare each angle to a right angle (90°) - imagine the corner of a square or rectangle. If the angle looks sharper or more pointed than a right angle, it's acute (less than 90°).

Q: What if one angle looks close to 90°?

If any angle appears to be exactly 90° or larger, the triangle is not acute! An acute triangle requires all three angles to be less than 90°.

Q: Can a triangle have two obtuse angles?

No! A triangle can have at most one obtuse angle because the sum of all angles in any triangle equals $180^\circ$. Two obtuse angles would exceed this limit.

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

Acute: All angles $90^\circ$Right: One angle = $90^\circ$Obtuse: One angle > $90^\circ$

Triangle Classification with Visual Angle Assessment

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

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Step-by-step video solution

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00:03 Let's see if the triangle in the drawing is acute-angled.

00:08 In the drawing, all angles look less than 90 degrees, so they are acute.

00:14 That means the triangle is acute-angled. And that's how we find the solution!

Step-by-step written solution

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Understand the problem

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

Step-by-step solution

An acute-angled triangle is defined as a triangle where all three interior angles are less than $90^\circ$ .

In examining the visual depiction of the triangle provided in the problem, we need to see if it appears to satisfy this property. The assessment relies on observing the triangle's structure shown in the drawing and noting any geometric indications suggesting angle types.

Given the information from the drawing, if all angles seem to satisfy the condition of being less than $90^\circ$ , then by definition, the triangle is an acute-angled triangle.

Conclusively, the answer to whether the triangle is acute-angled based on provided visual assessment and inherent assumptions in its illustration is: Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Acute triangles have all three angles less than $90^\circ$
Technique: Examine each angle visually - look for sharp corners without right angles
Check: Verify no angle appears to be $90^\circ$ or greater than $90^\circ$ ✓

Common Mistakes

Avoid these frequent errors

Assuming triangles are acute without checking all angles
Don't look at just one or two angles and assume the triangle is acute = wrong classification! One obtuse or right angle makes the entire triangle non-acute. Always examine all three angles carefully to ensure each is less than 90°.

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 less than 90° just by looking?

Compare each angle to a right angle (90°) - imagine the corner of a square or rectangle. If the angle looks sharper or more pointed than a right angle, it's acute (less than 90°).

What if one angle looks close to 90°?

If any angle appears to be exactly 90° or larger, the triangle is not acute! An acute triangle requires all three angles to be less than 90°.

Can a triangle have two obtuse angles?

No! A triangle can have at most one obtuse angle because the sum of all angles in any triangle equals $180^\circ$ . Two obtuse angles would exceed this limit.

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

Acute: All angles < $90^\circ$
Right: One angle = $90^\circ$
Obtuse: One angle > $90^\circ$

Why does the visual assessment matter in this problem?

Since we're not given specific angle measurements, we must rely on visual analysis of the triangle's shape. This helps develop your geometric intuition for recognizing angle types!

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