Difficulty: Easy

Average Score: 100%

In the xy-plane shown, triangle ABC is to be reflected over the x-axis to form triangle A'B'C'. Then triangle A'B'C' is to be reflected over the v-axis to form triangle A''B''C''.

Which TWO of the following nets are nets for the regular triangular pyramid show?

Rationale

A) ultq120opa-adms.png and C) ultq120opc-adms.png are nets for the regular triangular pyramid.

These two nets correctly depict the arrangement of faces required to construct a regular triangular pyramid, which consists of a triangular base and three triangular lateral faces.

A (ultq120opa-adms.png) CORRECT

This net showcases one triangular base with three triangular faces arranged around it. The configuration allows for successful folding into a three-dimensional triangular pyramid, meeting the definition of a regular triangular pyramid.

B (ultq120opb-adms.png) YOUR ANSWER

This net fails to represent a regular triangular pyramid because it does not include the correct number of triangular faces. A valid pyramid must have one base and three lateral faces, but this net appears to lack the necessary structure to achieve that form.

C (ultq120opc-adms.png) CORRECT

This net correctly illustrates one triangular base and three triangular lateral faces, allowing it to be folded into a regular triangular pyramid. The arrangement adheres to the geometric requirements of the pyramid's construction.

D (ultq120opd-adms.png) YOUR ANSWER

This net is unsuitable for forming a regular triangular pyramid as it does not maintain the necessary configuration of one base and three triangular faces. The arrangement does not allow for proper assembly into the three-dimensional shape required.

Conclusion

The correct nets for constructing a regular triangular pyramid are A) ultq120opa-adms.png and C) ultq120opc-adms.png. Both nets feature the requisite triangular base and three triangular lateral faces essential for forming the pyramid. The other choices do not conform to the necessary geometric properties, confirming their ineligibility as nets for the desired three-dimensional shape.

Which TWO of the following nets are nets for the regular triangular pyramid show?

A) ultq120opa-adms.png and C) ultq120opc-adms.png are nets for the regular triangular pyramid.

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