CAVALIERI'S PRINCIPLE

True

False - if two objects have equal volume must have the same BASE, not height

False - if two objects have equal volume must have the same SLANT HEIGHT, not height

False - if two objects have the same base and height, they must have the same volume.

True

False - an oblique shape and a right shape can never have the same volume

False - an oblique shape and a right shape can't have the same base

False - an oblique shape will always have the same volume as a right shape if they have the same base AND height

True

False - the cross sectional areas are not relevant

False - only the slant height is relevant

False - even if they have the same cross sectional areas and heights, they cannot have the same volume.

These COULD have the same volume

These MUST have the same volume

These MUST NOT have the same volume

Not enough information

These COULD have the same volume

These MUST have the same volume

These MUST NOT have the same volume

Not enough information

These COULD have the same volume

These MUST have the same volume

These MUST NOT have the same volume

Not enough information

These COULD have the same volume

These MUST have the same volume

These MUST NOT have the same volume

Not enough information

These COULD have the same volume

These MUST have the same volume

These MUST NOT have the same volume

Not enough information

How to calculate the area of the triangles

That the two triangles have the same area

That parallel lines show the angles are congruent, therefore the triangles are congruent by ASA

How to apply the pythagorean theorem

Rectangular Pyramid and Triangular Prism

Rectangular Pyramid and Cylinder

Triangular Prism and Cylinder

All three.

Rectangular Pyramid and Triangular Prism

Rectangular Pyramid and Cone

Triangular Prism and Cone

All three.

No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.