1. Consider the transformations below. Which transformations preserve distance? Which transformations preserve angle measure? Use your knowledge of rigid transformations to compare and contrast congruency and similarity. 1. Translation II. Reflection III. Rotation IV. Dilation 2. if triangle ABC ~ triangle LMN and triangle LMN ~ triangle XYZ is triangle ABC ~ triangle XYZ use the AA similarity criterion to support your answer. 3. suppose that a line that appears parallel to side BC of triangle ABC intersects sides AB and AC at points X and Y respectivily, and AX/AB =1/2. How can you determine if the line is or is not parallel to line BC? Explain.​

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)