Use a compass and straightedge to construct the bisector of ZA shown below. [Leave all construction marks.] A

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.

If possible, draw an equilateral and concave: a triangle c pentagon

Generalize your findings in Exercise 33. 33. Can you use the construction for the midpoint of a segment to divide a line segment into a three congruent parts? c six congruent parts? b four congruent parts? d eight congruent parts?

Use your compass and straightedge to bisect EF.

Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle. Exercises 34. 35

a If mAB=88, then mACB=____________. b If mAB=92 and C is the midpoint of major are ACB, then mAC=_____________.

Can you use the construction for the midpoint of a segment to divide a line segment into a three congruent parts? c six congruent parts? b four congruent parts? d eight congruent parts?

Consider a regular hexagon RSTUVW. What does intuition tell you about RTV, the result of drawing diagonals RT, TV, and VR?

Which formula would you use to establish each of the following claims? a The coordinates of X are d,c. b mVT-=0 c VT-RS- d The length of RV- is 2d2+c2 Trapezoid RSTV; X is the midpoint of RV-.