3. The diagram at right shows parallelogram QRVU, with diagonal QV drawn. Prove that VQU = {QVR. [hint: prove triangles congruent first!] U

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.

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

Using as few variables as possible, state the coordinates of each point if DEF is isosceles with DEF is an isosceles triangle with D(,_),E(,_),F(,_).

Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.

Classify as true or false: a If the vertex angles of two isosceles triangles are congruent, the triangles are similar. b Any two equilateral triangles are similar.

In the illustration, point M is the midpoint of the hypotenuse of right triangle AOB. Show that the area of rectangle OLMN is one-half of the area of triangle AOB.

Consider regular pentagon RSTVQ not shown. Given that diagonals QT and VR intersect at point F, show that VFFR=TFFQ.

A carpenter has placed a square over an angle in such a manner that ABAC and BDCD. In the drawing, what can you conclude about the location of point D?