CP - Proving Constructions Lesson

Math_Lesson_TopBanner.png Proving Constructions

Since you measure distances with your compass, you know that when you perform constructions you have congruent distances. You can use these congruent distances to make congruent triangles. Now, through CPCTC, you can prove that angles are congruent or that you have right angles. You can also prove that any particular construction you are performing actually does produce the figure you set out to construct.

For Example: You can easily argue that (when copying a segment) since you do not change the measure of the compass, you really do construct a congruent segment.

image of a copied and congruent segment

Then, since you used this same segment copying construction repeatedly, you know that all 4 sides are congruent and so you really did produce a rhombus.

Now use what you know about congruent triangles to prove that the construction for a perpendicular bisector really works.

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