Question

1. draw the net of the following 3 - d objects and show what sides are equal.

a.
b.

Explanation:

Step1: Analyze the triangular prism (a)

A triangular - prism net has two triangular faces and three rectangular faces. The two triangular faces are congruent. Among the rectangular faces, the rectangles that are adjacent to the equal - length sides of the triangular bases are equal in size.

Step2: Analyze the rectangular prism (b)

A rectangular prism net has 6 rectangular faces. Opposite faces are equal. The top and bottom faces are equal, the front and back faces are equal, and the two side faces are equal.

Since this is a drawing - related problem and cannot be fully presented in text, the following is a description of the equal - side relationships:
For the triangular prism (a): The two triangular bases are congruent. If the triangular base is isosceles or equilateral, the corresponding sides of the two bases are equal. Also, the rectangles attached to the equal - length sides of the triangular bases are equal.
For the rectangular prism (b): Opposite rectangular faces are equal. That is, if the length is \(l\), width is \(w\), and height is \(h\), the faces with dimensions \(l\times w\), \(l\times h\), and \(w\times h\) have their opposite counterparts with the same dimensions.

Answer:

For the triangular prism (a): The two triangular bases are equal. Some of the rectangular faces may be equal depending on the base triangle's side - lengths.
For the rectangular prism (b): Opposite rectangular faces are equal.