LEARN · EXPLAIN · REVISE

Does having two parallel faces alone guarantee a prism? Explain.

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 8.1 · PDF 104 / printed page 97

TOPIC 01

Basic solid figures

Build understanding of basic solid figures through definitions, contrasting cases and justified applications.

Use definitions, valid spatial reasoning and metric checks for basic solid figures.
Connect representations and justify the steps, including boundary cases.
Explain a solution and apply the idea to a changed situation.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Identify the defining faces, cross-sections and generating elements of the solid.

Hint 2

Consider a frustum cut parallel to a pyramid base.

Worked solution

Identify the defining faces, cross-sections and generating elements of the solid.
A truncated pyramid can have parallel but unequal bases, so it is a counterexample.
A necessary visible feature need not be a sufficient definition.

No. The bases must also be congruent polygons and the lateral edges parallel in the prism structure.

Checks and common pitfalls: A necessary visible feature need not be a sufficient definition.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use definitions, valid spatial reasoning and metric checks for basic solid figures.
Defining structures: Prisms, pyramids, frustums and solids of revolution have different defining base and side relations.
Sections: Parallel sections of a pyramid are similar; metric ratios depend on distance from the apex.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Prisms, pyramids, frustums and solids of revolution have different defining base and side relations.
Expected reasoning: Parallel sections of a pyramid are similar; metric ratios depend on distance from the apex.
Expected correction: Two parallel faces alone do not define a prism.