Triangle Geometry: Is it Possible to Have Two 90-Degree Angles in One Triangle?

Q: Why can't a triangle have two 90° angles if rectangles can have four?

Great question! Rectangles are quadrilaterals with 4 sides and their angles sum to 360°, so four 90° angles work perfectly. Triangles only have 3 sides and their angles must sum to exactly 180°.

Q: What would happen if I tried to draw a triangle with two right angles?

You'd end up with two perpendicular lines that never close to form a triangle! The third side would need to be a straight line, creating a 180° angle, which isn't possible in a triangle.

Q: Can a triangle have one right angle?

Yes! A right triangle has one 90° angle and two other angles that add up to 90°. For example: 90° + 60° + 30° = 180°. This works perfectly!

Q: Are there any shapes that can have two right angles?

Absolutely! Quadrilaterals like rectangles, squares, and trapezoids can have two or more right angles because their angles sum to 360°, giving plenty of 'room' for multiple 90° angles.

Q: How do I remember that triangle angles sum to 180°?

Think of it as half a circle! A full circle is 360°, so a triangle (which looks like half) is 180°. You can also remember: 3 sides = 180° (3 × 60° = 180°).

Triangle Properties with Angle Sum Constraints

Can a triangle have two right angles?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether a triangle can have 2 right angles?

00:04 Mark the triangle's angles as A,B,C

00:12 The sum of angles in a triangle equals 180

00:17 Substitute 2 angles of 90° (right angles)

00:29 Isolate the remaining angle C

00:35 It turns out it needs to be equal to 0

00:39 There's no such thing as a line with 0 angle, therefore it's impossible

00:43 That's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Can a triangle have two right angles?

Step-by-step solution

The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Angle Sum Rule: All three angles in any triangle always equal 180°
Right Angle Check: Two 90° angles would total 180° leaving 0° for third angle
Verification: 90° + 90° + 0° = 180° but 0° cannot form triangle ✓

Common Mistakes

Avoid these frequent errors

Thinking triangles can have two right angles like rectangles
Don't assume triangles follow the same rules as quadrilaterals = impossible triangle! Rectangles have 360° total, but triangles only have 180°. Always remember that triangles need exactly three angles that sum to 180°.

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

Why can't a triangle have two 90° angles if rectangles can have four?

Great question! Rectangles are quadrilaterals with 4 sides and their angles sum to 360°, so four 90° angles work perfectly. Triangles only have 3 sides and their angles must sum to exactly 180°.

What would happen if I tried to draw a triangle with two right angles?

You'd end up with two perpendicular lines that never close to form a triangle! The third side would need to be a straight line, creating a 180° angle, which isn't possible in a triangle.

Can a triangle have one right angle?

Yes! A right triangle has one 90° angle and two other angles that add up to 90°. For example: 90° + 60° + 30° = 180°. This works perfectly!

Are there any shapes that can have two right angles?

Absolutely! Quadrilaterals like rectangles, squares, and trapezoids can have two or more right angles because their angles sum to 360°, giving plenty of 'room' for multiple 90° angles.

How do I remember that triangle angles sum to 180°?

Think of it as half a circle! A full circle is 360°, so a triangle (which looks like half) is 180°. You can also remember: 3 sides = 180° (3 × 60° = 180°).

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