How do I solve a proof that has Given: angle 5 is complementary to angle 7. Prove: MI is perpendicular to IE.

Question

It also gives me a diagram that has what looks like a right angle (MIE) and a line (K) that is in the interior of the angle.

Answer 1

Hi Sydney, it's hard to be 100% sure without seeing the diagram that goes with the question. But based on how you have described it, I am assuming that <MIK is labeled as 5 and <KIE is labeled as 7 or vice-versa. In this case, it is probably a pretty short proof.

Statement 1 would be "Angle 5 is Complementary to Angle 7" and the reason would be "Given".

Statement 2 would be something like "Measure of Angle 5 plus Measure of Angle 7 = 90" and the reason "definition of complementary angles".

Then, Statement 3 along the lines of "Angle MIE is a right angle" with reason "Definition of Right Angle" or the reason could be said like this: "An Angle is a Right Angle if and only if the measure of that angle is 90 degrees".

Finally, Statement 4 "MI is Perpendicular to IE" with a reason like "Definition of Perpendicular" or maybe this reason could be "Two lines meet to form a Right Angle if and only if those two lines are Perpendicular".

And you can put that in whatever format is normal for your class....two-column proof, paragraph proof, etc.

I hope this is helpful. If there is something more complicated going on with the diagram, let me know and I can try to explain further or refine this answer. :)