Certain pairs of triangles are shown below. The column heading represents various theorems used to prove triangles are similar. Identify which theorem is appropriate to prove each pair of triangles similar and then classify the triangles under the column heading.
Figure 1
Figure 2:
V47
12
Figure 3:
Figure 4
18
21
15
B

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)

The measures of the angles in △abc are given by the expressions in the table. angle measure angle a 65° angle b (3x−10)° angle c (2x)∘ find the value of x. then find the m∠b and m∠c.

You are living in aldine, tx and you are planning a trip to six flags in arlington, tx. you look on a map that has a scale of 0.5 inches to 30 miles. if the map shows the scale distance from aldine to arlington is 4 inches, how far is the actual distance?