Triangle Classification: Identifying an Acute-Angled Triangle from Diagram

Q: What does the small square symbol in the corner mean?

The small square symbol is the universal mathematical notation for a right angle, which measures exactly $90^\circ$. Whenever you see this symbol, you know that angle is a right angle!

Q: Can a triangle be both acute and right-angled?

No, absolutely not! A triangle can only be classified as one type: acute (all angles 90°). These categories are mutually exclusive.

Q: How can I tell if a triangle is acute just by looking at it?

You cannot reliably determine if a triangle is acute just by its appearance! You must either measure the angles or look for angle markings in the diagram. Visual estimation can be very misleading.

Q: What makes a triangle acute versus obtuse?

Acute triangle: ALL three angles are less than 90°Right triangle: ONE angle equals exactly 90°Obtuse triangle: ONE angle is greater than 90°

Q: Why isn't this triangle acute if it looks pointy?

Even though the triangle might look sharp or pointy, the presence of the right angle symbol (small square) tells us definitively that one angle is 90°. This makes it a right triangle, not an acute triangle!

Triangle Classification with Angle Identification

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 in the drawing 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

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Understand the problem

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

Step-by-step solution

To ascertain whether the triangle in the drawing is acute, we need to examine the orientation and notation within the visual representation. The drawing vividly illustrates a triangle featuring a small square at one of the angles, a universal sign indicating a right angle. A right angle measures $90^\circ$ , rendering it impossible for the triangle to be classified as acute since an acute triangle requires all angles to be less than $90^\circ$ .

Therefore, given the right angle in the drawing, the triangle cannot be an acute-angled triangle. Consequently, the correct choice is:

No (:

)

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Acute triangles have all angles measuring less than 90°
Technique: Look for right angle symbol (small square) indicating 90°
Check: If any angle equals or exceeds 90°, triangle is not acute ✓

Common Mistakes

Avoid these frequent errors

Ignoring the right angle symbol in diagrams
Don't assume a triangle is acute just by looking at its shape without checking angle markers = wrong classification! The small square symbol specifically indicates a 90° angle, which automatically makes it a right triangle, not acute. Always examine all angle markings and symbols carefully.

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

What does the small square symbol in the corner mean?

The small square symbol is the universal mathematical notation for a right angle, which measures exactly $90^\circ$ . Whenever you see this symbol, you know that angle is a right angle!

Can a triangle be both acute and right-angled?

No, absolutely not! A triangle can only be classified as one type: acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°). These categories are mutually exclusive.

How can I tell if a triangle is acute just by looking at it?

You cannot reliably determine if a triangle is acute just by its appearance! You must either measure the angles or look for angle markings in the diagram. Visual estimation can be very misleading.

What makes a triangle acute versus obtuse?

Acute triangle: ALL three angles are less than 90°

Right triangle: ONE angle equals exactly 90°

Obtuse triangle: ONE angle is greater than 90°

Why isn't this triangle acute if it looks pointy?

Even though the triangle might look sharp or pointy, the presence of the right angle symbol (small square) tells us definitively that one angle is 90°. This makes it a right triangle, not an acute triangle!

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