Question

1. here are two three - dimensional figures. a b tell whether each of the following statements describes figure a, figure b, both, or neither. a. this figure is a polyhedron. b. this figure has triangular faces. c. there are more vertices than edges in this figure. d. this figure has rectangular faces. e. this figure is a pyramid. f. there is exactly one face that can be the base for this figure. g. the base of this figure is a triangle. h. this figure has two identical and parallel faces that can be the base.

Explanation:

Step1: Define polyhedron

A polyhedron is a 3 - D shape with flat faces. Both A and B have flat faces.

Step2: Check triangular faces

Both A (triangular ends) and B (triangular faces) have triangular faces.

Step3: Analyze vertices and edges

For 3 - D shapes, usually edges are more than vertices or follow Euler's formula $V - E+F = 2$. So neither has more vertices than edges.

Step4: Identify rectangular faces

Figure A has rectangular faces, B does not.

Step5: Define pyramid

A pyramid has a base and triangular faces that meet at a vertex. Figure B is a pyramid, A is a prism.

Step6: Determine single - base face

In a pyramid (Figure B), there is exactly one base face.

Step7: Check triangular base

Both A (triangular ends) and B (triangular base) have a triangular base.

Step8: Identify parallel and identical bases

A prism (Figure A) has two identical and parallel bases.

Answer:

a. Both
b. Both
c. Neither
d. Figure A
e. Figure B
f. Figure B
g. Both
h. Figure A