70. Meet the Prism · Two congruent bases, parallel sides

Try to break it

Drag the vertices A, B, or C to reshape the prism. Notice how the back base and side faces adjust automatically—they stay congruent and parallel. Try to break it! You'll find the definition holds tight.

How you build it

Construct a prism.

• Place point A, the first vertex of the base triangle.
• Place point B, the second base vertex.
• Place point C, the third base vertex.
• Draw the base side from A to B.
• Draw the base side from B to C.
• Draw the base side from C to A to close the front triangle.
• Place point D — the first vertex of the top base — up and to the right of A. This sets how deep the prism is.
• Place point E — the top vertex matching B. Shift B by the same amount and direction that took A to D, so edges AD and BE are equal and parallel.
• Place point F — the top vertex matching C. Shift C by the same amount and direction, so all three side edges AD, BE and CF are equal and parallel.
• Draw the back side from D to E.
• Draw the back side from E to F.
• Draw the back side from F to D to close the back triangle.
• Draw the lateral edge from A to D.
• Draw the lateral edge from B to E.
• Draw the lateral edge from C to F to complete the prism.

The proof, step by step

Prove that the solid is a prism — two congruent, parallel bases.

• Identify the two bases: they are congruent polygons (triangles here).
• Check the lateral faces: they are parallelograms formed by connecting corresponding vertices.
• Verify parallelism: the bases are parallel, and lateral edges are parallel to each other.

Worked example

A prism has two congruent and parallel bases. If the base is a pentagon, how many lateral faces does the prism have?

The number of lateral faces equals the number of sides of the base. A pentagon has 5 sides, so the prism has 5 lateral faces.

• 5 — correct
• 6
• 10
• 15