Consider three lines K, L and M intersecting at a point O as shown. Line K contains the points A and D, L contains the points B and E while M contains the points C and F. Show that if AB is parallel to DE and CB is parallel to FE, then AC must be parallel to DF. In this situation, the triangles ABC and DEF are said to be in perspective. A K B E L F M

For a given triangle such as ABC, what word describes the point of concurrency for athe three perpendicular bisectors of sides? _____________ bthe three altitudes? ____________________

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.

Which type of path straight, curved, circular, or scattered is determined by: a a roller coaster? b a pencil? c a carousel? d darts thrown at a dartboard?

Given that mA=2x+y, mB=2x+3y-20, and mC=3x-y+16, find the measure of each angle of .

Given that mAB=106 and mDC=32, find: a m1 b m2

In the drawing, ABDCEF. Suppose that transversals l and m are also parallel. D and C are the midpoints of AE and BF, respectively. If parallelogram ABCD similar to parallelogram DCFE?

What relationship, if any, exists between two angles a with equal measures? b that have the same vertex and a common side between them?

In ABC,AC=5.3,BC=7.2 and BA=6.7. With angle bisectors as shown, which line segment is longer? a AE or EC? b CD or DB? c AF or FB?

In quadrilateral RSTU, RSST and UT diagonal RT. If RS=6, ST= 8, and RU = 15, determine UT.