Let ABC be an equilateral triangle and let M be a point that does not lie on the circle described on the triangle. Show that the distances AM, BM and CM can form sides of a triangle.

Is it possible to draw a triangle whose angles measure a. 100, 100, and 60? b. 45, 45, and 90?

Which lines, line segments, or rays are used to construct: a The incircle of a triangle? b The circumcircle of a triangle?

Two streets meet to form an obtuse angle at point B. On that corner, the newly poured foundation for a building takes the shape of a parallelogram. Which diagonal, AC- or BD-, is longer?

Which lines or line segments or rays must be drawn or constructed in a triangle to locate its aincenter? bCircumcenter? corthocenter? dcentroid?

a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.