Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. 

The following is a 3-step proof. Complete the proof. 

Given: \( \angle 1 = \angle 2 \) 

\( A P = B P\) 

Prove: \( \triangle A P D \cong \triangle B P C\) 

A sequence of transformations including a dilation was performed below. What is the scale factor of the dilation? 

Scale Factor \( = \) 

This container holds exactly 3 tennis balls. How much empty space is in the container if one tennis ball is removed as shown in the picture? Assume the height of the container is the same height as three tennis balls. Use \( 3.14 \) for pi. 

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost. 

Helpful information: 

h: height of cylinder, 

r : radius of cylinder 

Volume of a cylinder: \(V = \pi r ^ { 2 } h\) 

Area of the sides: \(A = 2 \pi r h\) 

Area of the top/bottom: \(A = \pi r ^ { 2 } \) 

To minimize the cost of the package: 

Radius: 

Height: 

Minimum cost: 

All diagonals from a single vertex of a hexagon are drawn. Four triangles will result. 

True 

False