Make constructions for each of the following. Remember this: A construction is a *method* that should produce the desired outcome *any time the given conditions are met.* So, making a construction that only works for special cases is not acceptable. Your method must work for *any potential situation* as long as that situation meets the given conditions.

Explain your constructions so that their logic is clear. Refer to *types of explanations* (geometry) for a reminder of what this means.

- Given: Point A, point B and a length m.

Construct the locus of points X such that the m= Dist(X,A) + Dist(X,B).

*That is, construct the locus of points such that m is the the sum of any point's distances from A and B.*

- Given: Point A, point B and a length m.

Construct the locus of points X such that the m= Dist(X,A) - Dist(X,B).

*That is, construct the locus of points such that m is the difference of any point's distances from A and B.*

- Given: Point A and line k.

Construct the locus of points X such that Dist(X,A) = Dist(X,k).

- Given segments of length a and b.

Construct a segment of length a*b. Click here for an example.

- Given: Point A, line k, and length m.

Construct the locus of points X such that m = Dist(X,A) + Dist(X,k)

- Given: Point A, line k, and length m.

Construct the locus of points X such that m = Dist(X,A) - Dist(X,k)

- Given: Quadrilateral ABCD.

Construct a point that is equidistant from all four sides.

*Click here (after Tuesday) to see what other students have done. Click here to see Jim Wilson's comments on a student's exploration.*

- Given: Points A, B, C, and D are midpoints of the sides of a quadrilateral.

Construct the quadrilateral. Click here for some hints.