Trapezoid Properties - Problem 1


In this problem we have an isosceles trapezoid which means we have two legs that are congruent when we have a pair of parallel sides. So let’s go over and take a look at what we know about isosceles trapezoids.

Well we see that the base angles, so if I’m looking at two base angles, they are going to be congruent to each other. We also know that the same side interior angles here, so I’m looking at these triangles right here, are going to be supplementary that’s the definition of same side interior.

So let's go back to our problem. If I look at the only thing that we know about this trapezoid that’s angle B which is 110 degrees, I could start of by finding angle C. Well I know that these two must be supplementary because they are on the same side of this transversal BC. So if B is 110 C must be what? 180 minus 110 which 70 degrees. So I’m going to write in here that C must be 70 degrees.

Now you just have to remember that your base angles are congruent to each other. So I’m going to write that D must be 70 degrees and on that A must be 110 degrees. So A we said was 110 and D we said was 70 degrees. The key thing here was remembering that same side interior angles are supplementary and that base angles in an isosceles trapezoid are always congruent.

parallel sides isosceles trapezoid base angles base