Mathematics

Question

Which statement is always true?
A cross section parallel to the base of a right rectangular prism is a square.
A cross section perpendicular to the base of a right rectangular prism is congruent to the base.
A cross section parallel to the base of a right rectangular prism is congruent to the base.
A cross section perpendicular to the base of a right rectangular prism has the same dimensions as the base.

2 Answer

  • From the given statements in this item, what is always true is that the cross section of parallel to the base of the right rectangular prism is congruent to the base. The answer is the third choice. This is because when we cut through any part of the prism parallel to the base, the shape of the cross section is the same as the base. 
  • Answer:

    A cross section parallel to the base of a right rectangular prism is congruent to the base.

    Step-by-step explanation:

    1. A cross section parallel to the base of a right rectangular prism is a square. This is false as the cross section will be a rectangle if the base is rectangular and square if the base is a square.

    2. A cross section perpendicular to the base of a right rectangular prism is congruent to the base. No, only parallel cross sections are similar to base.

    3. A cross section parallel to the base of a right rectangular prism is congruent to the base. This is true as a cross section parallel to any shape will give the shape of the base. With each slice, the size gets smaller but the shape is the same as base.

    4. A cross section perpendicular to the base of a right rectangular prism has the same dimensions as the base. This is false as a completely different shape is generated with different dimensions.

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