which pair of figures has the same number of faces as vertices?\no triangular prism and triangular…
which pair of figures has the same number of faces as vertices?\no triangular prism and triangular pyramid\no triangular prism and rectangular prism\no rectangular pyramid and triangular pyramid\no rectangular pyramid and rectangular prism
Answer
Explanation:
Step1: Recall faces and vertices of triangular prism
A triangular prism has 5 faces (2 triangular and 3 rectangular) and 6 vertices.
Step2: Recall faces and vertices of triangular pyramid
A triangular pyramid has 4 faces (all triangular) and 4 vertices.
Step3: Recall faces and vertices of rectangular prism
A rectangular prism has 6 faces (all rectangular) and 8 vertices.
Step4: Recall faces and vertices of rectangular pyramid
A rectangular pyramid has 5 faces (1 rectangular and 4 triangular) and 5 vertices.
Step5: Check pairs
- Triangular prism and triangular pyramid: 5 faces vs 4 faces, 6 vertices vs 4 vertices - not equal.
- Triangular prism and rectangular prism: 5 faces vs 6 faces, 6 vertices vs 8 vertices - not equal.
- Rectangular pyramid and triangular pyramid: 5 faces vs 4 faces, 5 vertices vs 4 vertices - not equal.
- Rectangular pyramid and rectangular prism: 5 faces vs 6 faces, 5 vertices vs 8 vertices - not equal. But rectangular pyramid has 5 faces and 5 vertices, and we are looking for a pair where the number - of - faces of one is equal to the number of vertices of the other and vice - versa. The pair with the same number of faces as vertices is the triangular pyramid (4 faces and 4 vertices) and the rectangular pyramid (5 faces and 5 vertices).