Question

Prove the following theorem indirectly. We will give you a start.. . Prove that a triangle cannot have two right angles.. A triangle cannot have two right angles. Suppose a triangle had two right angles.

Answer 1

It is given in the question that a triangle had two right angles. Now the question is, whether this is possible? It is already known that the sum of the three angles of any triangle is 180 degrees. Now if the two angles within a triangle is 90 degree each, then there is no possibility of having a third angle. This proves that a triangle cannot have more than one 90 degree angle.

Answer 2

Suppose a triangle had two right angles.
The sum of all angles of any triangle is 180°.
The measure of a right angle is 90°.
By difference, the measure of the other angle can be determined.
Since the two angles have a measure of 90° each, then by difference, the measure of the third angle is 180° - (90° + 90°) = 0°.
If the angle is 0°, there would only be two sides.
A triangle has three sides.
Therefore, a triangle can't have two right angles.