Right Triangle Properties: Can a Triangle Have a 90-Degree Angle?

Q: What's the difference between a right angle and a right triangle?

A right angle is a single 90° angle, while a right triangle is a triangle that contains one right angle. The triangle gets its name from having that special angle!

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

No! If a triangle had two 90° angles, that would be 180° already, leaving 0° for the third angle. Since angles in triangles must be greater than 0°, this is impossible.

Q: What are the other two angles in a right triangle?

The other two angles must be acute angles (less than 90°) and they must add up to exactly 90° since all three angles total 180°.

Q: Are right triangles common in real life?

Yes! Right triangles appear everywhere - in construction, architecture, navigation, and even in your smartphone screen corners. They're essential for calculating distances and heights.

Q: How can I remember what makes a triangle 'right'?

Think of a square corner - that's a right angle! A right triangle has one corner that looks exactly like the corner of a square or rectangle.

Triangle Classifications with Angle Measurements

Can a triangle have a right angle?

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Step-by-step video solution

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00:00 Determine whether a triangle can have a right angle

00:03 According to the drawing, we can see that such a triangle exists

00:06 We drew a right triangle

00:09 This is the solution

Step-by-step written solution

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Understand the problem

Can a triangle have a right angle?

Step-by-step solution

To determine if a triangle can have a right angle, consider the following explanation:

Definition of a Right Angle: An angle is classified as a right angle if it measures exactly $90^\circ$ .
Definition of a Right Triangle: A right triangle is a type of triangle that contains exactly one right angle.
According to the definition, a right triangle specifically includes a right angle. This is a well-established classification of triangles in geometry.

Thus, a triangle can indeed have a right angle and is referred to as a right triangle.

Therefore, the solution to the problem is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: A right triangle contains exactly one 90° angle
Classification: Triangles are named by their largest angle type
Verification: Sum of all three angles must equal 180° ✓

Common Mistakes

Avoid these frequent errors

Thinking triangles cannot have 90° angles
Don't assume all triangles must have only acute angles = missing an entire triangle category! This ignores right triangles, which are fundamental in geometry. Always remember that triangles can be acute, right, or obtuse based on their largest angle.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

What's the difference between a right angle and a right triangle?

A right angle is a single 90° angle, while a right triangle is a triangle that contains one right angle. The triangle gets its name from having that special angle!

Can a triangle have more than one right angle?

No! If a triangle had two 90° angles, that would be 180° already, leaving 0° for the third angle. Since angles in triangles must be greater than 0°, this is impossible.

What are the other two angles in a right triangle?

The other two angles must be acute angles (less than 90°) and they must add up to exactly 90° since all three angles total 180°.

Are right triangles common in real life?

Yes! Right triangles appear everywhere - in construction, architecture, navigation, and even in your smartphone screen corners. They're essential for calculating distances and heights.

How can I remember what makes a triangle 'right'?

Think of a square corner - that's a right angle! A right triangle has one corner that looks exactly like the corner of a square or rectangle.

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