SOLUTION: If angle 1 and angle 3 are supplementary, is triangle ABC iscoscles? I say yes but how do I prove it?

Question 72592: If angle 1 and angle 3 are supplementary, is triangle ABC iscoscles? I say yes but how do I prove it?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Think about this a minute!
.
If angle 1 and angle 3 are supplementary, what is their sum? (Use the definition of supplementary.)
.
What is the sum of the three angles of a triangle?
.
What has to be the measure of angle 2 in the triangle?
.
A more appropriate question than, "is the triangle isosceles?" would have been "is there a triangle.
.
Now that you've thought about it a bit, angles 1 and 3 by being supplementary add up to
180 degrees by definition. The three angles of a triangle add up to be 180 degrees.
So the "third" angle of the triangle would have to be 0 degrees so that when it is added
to the supplementary angles the sum does not go over 180 degrees. And if one of the angles
of a triangle is zero degrees, you really don't have a triangle at all.
.
Hope this helps you to understand this problem a little better. If you still can't see
it, try this as an exercise. Two right angles are supplementary. Try making a triangle
where two of the angles are 90 degrees. Maybe that will give you some further insight into
the problem.

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