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How are the volumes of cones and pyramids related to the volumes of prisms and cylinders?
A cone is 1/3 of the volume of a cylinder with the same base and height. A pyramid is 1/3 of the volume of a prism with the same base and height.
Are two scalene triangles always similar?
yes. they are always the same but a different scale.
What is the relationship between the height and base area?
There is no relationship, in the sense that you can have any base are with any height. For a prism shape (if the horizontal cross section is always the same as the base), the base area times the height is equal to the volume.
Is two regular polygons always sometimes or never similar?
If they have the same nuber of sides (angles) then always. If not then never. So, overall, I suppose the answer is sometimes - depending on the number of sides.
Is it true to say that two equiangular triangle are always equal?
No. Equiangular only implies the angles are the same, but says nothing about the lengths. Two equiangular triangles are always similar, only sometimes congruent.
