Indirect proof given triangle ABC,<B is an obtuse angle prove there can only be one obtuse angle in triangle.

Obtuse angles are greater than 90 degrees.

The sum of all angles in a triangle must be 180 degrees. You can't have two of them > 90 and have a total of 180.

Another indirect proof: try drawing one.

yes

To prove that there can only be one obtuse angle in triangle ABC, given that angle B is obtuse:

Step 1: Write down the given information:
- Triangle ABC
- Angle B is obtuse

Step 2: Understand the concept:
- An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees.
- In a triangle, the sum of the three angles is always 180 degrees.

Step 3: State the theorem to be proved:
- The statement to be proved is that there can only be one obtuse angle in triangle ABC.

Step 4: Start the proof:
Since the sum of the three angles in a triangle is always 180 degrees, let's assume that there are two obtuse angles in triangle ABC, denoted as angles X and Y.

Step 5: Write the equation representing the sum of the angles in triangle ABC:
Angle A + Angle B + Angle C = 180 degrees

Step 6: Substitute the angle measures into the equation:
Angle A + Angle X + Angle Y + Angle C = 180 degrees

Step 7: Rearrange the equation:
Angle A + Angle C = 180 degrees - Angle X - Angle Y

Step 8: Analyze the equation:
Since angle X and angle Y are both obtuse angles, their measures are greater than 90 degrees. Thus, the sum of Angle X and Angle Y is greater than 180 degrees.

Step 9: Conclusion:
We have arrived at a contradiction. The sum of angles A and C cannot equal a negative number, as the left side of the equation must be positive. Therefore, our assumption that there are two obtuse angles in triangle ABC is incorrect.

Step 10: State the final claim:
Based on the contradiction, we can conclude that there can only be one obtuse angle in triangle ABC.

To prove that there can only be one obtuse angle in triangle ABC, given that angle B is obtuse, you can use an indirect proof.

1. Assume that there are two obtuse angles in triangle ABC, let's say angle B and angle X.

2. Since we assumed that angle B is obtuse, it means angle B is greater than 90 degrees.

3. By definition, the sum of all angles in a triangle is always 180 degrees.

4. If there are two obtuse angles (B and X), it means the sum of those angles would be more than 180 degrees, which contradicts the fact that the sum of angles in a triangle is always 180 degrees.

5. Hence, our assumption that there are two obtuse angles in triangle ABC is incorrect.

6. Therefore, there can only be one obtuse angle in triangle ABC, and in this case, it is angle B since we assumed it to be obtuse initially.

This completes the indirect proof, and we have proved that there can only be one obtuse angle in triangle ABC, given that angle B is obtuse.