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Perpendicular Proofs

Algebraic Proof

What is the shortest distance between point C and Line AB? Round answers to the nearest hundredth. Prove that it's the shortest distance possible.

Construction

Construct a line that is perpendicular to line AB and passes through point C. What about your construction proves the lines are perpendicular?
Construct a line that is perpendicular to line AB and passes through point C. What about your construction proves the lines are perpendicular?

Geometric Proof

What are the measures of angles 1, 2, 3, and 4? Prove each measurement using theorems we've covered in class and proper geometric vocabulary.

Two lines,Ā aĀ andĀ b, are perpendicular to lineĀ c. LineĀ dĀ is parallel to lineĀ c. The distance between linesĀ aĀ andĀ bĀ isĀ xĀ meters. The distance between linesĀ cĀ andĀ dĀ isĀ yĀ meters. What shape is formed by the segments between the points ofĀ intersectionĀ of the four lines? How do you know?

Real world

You are building a new room in a house (you may choose whether this is your house, you are a contractor, building a model for a project, or creating a set peace for a TV show). You need the walls to all meet at right angles, but someone has ruined you square (a measuring tool for making right angles). Someone is coming to inspect your work today and you're not sure when they'll arrive. So, there's no time in the moment to run to the store. How could you ensure that the wall you're about to build is in fact perpendicular to the previous wall?