Geometric Analysis: Identifying Acute Triangles from Diagrams

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

Look for square corners that form an "L" shape. Right angles appear perfectly square, while acute angles look sharper and more pointed than a corner of a square.

Q: What if the triangle looks close to having a right angle?

Trust your visual assessment! If it looks slightly pointed rather than perfectly square, it's likely acute. In diagrams, right angles are usually drawn to look obviously square.

Q: Can a triangle have two obtuse angles?

No! This is impossible. The sum of angles in any triangle is $ 180^\circ $. Two obtuse angles (each > $ 90^\circ $) would already exceed this limit.

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

Acute: All angles $ 90^\circ $ (all sharp)Right: One angle = $ 90^\circ $ (one square corner)Obtuse: One angle > $ 90^\circ $ (one wide angle)

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

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is acute-angled

00:03 According to the drawing, this angle appears to be right angled (90°)

00:12 Proceed to mark the other angles as A,B

00:20 The sum of angles in a triangle equals 180 degrees

00:28 Isolate the remaining angles

00:42 The 2 angles are less than 90 degrees which is consistent with a right angle triangle

00:47 The triangle is right-angled, and this is the solution to the question

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

To solve this problem, we need to determine if the triangle depicted is an acute-angled triangle.

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

Upon observing the triangle in the drawing, it appears that each of its angles is less than $90^\circ$ . The shape of the triangle does not present any right angles ( $90^\circ$ ) or angles greater than $90^\circ$ .

Thus, based on the visual inspection and understanding of triangle properties, the triangle appears to be acute-angled.

Therefore, the solution to the problem is Yes, the triangle is an acute-angled triangle.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Acute Definition: All three angles must be less than $90^\circ$
Visual Method: Look for sharp corners - no right angles or wide obtuse angles
Verification: Check each vertex appears pointed, not square or wide ✓

Common Mistakes

Avoid these frequent errors

Assuming one acute angle means the triangle is acute
Don't focus on just one sharp angle = wrong classification! A triangle needs ALL three angles to be acute to be classified as acute-angled. Always examine every single angle in the triangle before concluding.

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 just by looking?

Look for square corners that form an "L" shape. Right angles appear perfectly square, while acute angles look sharper and more pointed than a corner of a square.

What if the triangle looks close to having a right angle?

Trust your visual assessment! If it looks slightly pointed rather than perfectly square, it's likely acute. In diagrams, right angles are usually drawn to look obviously square.

Can a triangle have two obtuse angles?

No! This is impossible. The sum of angles in any triangle is $180^\circ$ . Two obtuse angles (each > $90^\circ$ ) would already exceed this limit.

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

Acute: All angles < $90^\circ$ (all sharp)
Right: One angle = $90^\circ$ (one square corner)
Obtuse: One angle > $90^\circ$ (one wide angle)

Do I need to measure the angles with a protractor?

Not for this type of question! You can classify triangles by visual inspection. The drawing gives you enough information to identify the triangle type without precise measurements.

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