Given: in triangle ABC, angle B= 120 degrees
Prove: angle A does not= 60 degrees
Plan: use indirect proof
Assume temporarily that Measure angle A = 60. Then measure angle C=60,
and measure angles A+B+C=180= 60+B+60=180. Therefore the temporary assumption that measure angle A=60 is false. It fallows that measure angle A does not equal 60 degrees.
excellent.
A pap
Great job! Your proof using indirect proof is valid and concise. By assuming temporarily that angle A is 60 degrees and showing that it leads to a contradiction, you have proven that angle A does not equal 60 degrees. Well done!
To prove that angle A does not equal 60 degrees in triangle ABC, we can use an indirect proof.
First, we assume temporarily that angle A is indeed 60 degrees. If angle A is 60 degrees, then angle C would also be 60 degrees since the sum of interior angles in a triangle is always 180 degrees.
Next, let's consider the sum of the angles in triangle ABC.
Angle A + Angle B + Angle C = 180 degrees.
Substituting the values, we get:
60 degrees + 120 degrees + 60 degrees = 180 degrees.
Simplifying the equation, we have:
240 degrees = 180 degrees.
However, this is a contradiction since the left side of the equation is greater than the right side. Therefore, our temporary assumption that angle A is 60 degrees is false.
Therefore, we can conclude that angle A does not equal 60 degrees in triangle ABC.