Question

apply it
use what you learned to solve these problems.
6 each line segment in the net shown is labeled with a letter. the net will be cut out and folded to form a triangular pyramid. which line segment will match up with segment a to form an edge of the pyramid? show your work.
solution
7 issay cuts out the net shown and folds it to make a three - dimensional shape. which three - dimensional shape does issay make?
a right triangular prism
b right rectangular prism
c pyramid with a triangular base
d pyramid with a rectangular base

Explanation:

Question 6 (assuming we analyze the net folding for triangular pyramid edge matching, though the diagram is partial, we can reason about triangular pyramid nets):

Step1: Recall triangular pyramid net

A triangular pyramid (tetrahedron) net has 4 triangular faces. When folded, edges that are adjacent in the 3D shape must be equal and match in the net.

Step2: Identify matching edges

In a triangular pyramid net, each edge of a triangular face will match with an edge of another triangular face when folded. For segment \( A \), we look for the segment that is congruent and positioned to fold onto \( A \). Typically, in such nets, the edge that is a corresponding side of a congruent triangle (since all faces of a regular triangular pyramid are equilateral triangles, or in a general one, congruent/equal-length edges) will match. If we assume the net has triangles where \( A \) is a side, the segment with the same length and adjacent in the folding pattern (e.g., the other side of a triangle that will be glued to \( A \)'s triangle) will match. (Since the diagram is partial, but conceptually, we can say that the segment equal in length and part of the adjacent triangular face in the net will match. For example, if \( A \) is a side of a triangle, the corresponding side of the triangle that shares a common vertex and will be folded to meet \( A \) is the match.)

Question 7:

To determine the 3D shape from the net, we analyze the net's components. A right triangular prism net has two triangular bases and three rectangular lateral faces. A right rectangular prism has six rectangular faces. A pyramid has a base and triangular lateral faces (number of lateral faces equals number of base sides). The net for a right triangular prism has 2 triangles (bases) and 3 rectangles (lateral faces). If Issay's net has 2 triangular faces and 3 rectangular faces, folding it forms a right triangular prism. Option A is correct because a right triangular prism's net consists of two congruent triangles (bases) and three rectangles (lateral faces), which when folded, create the prism. Options B (rectangular prism) would have rectangular bases, C and D (pyramids) have a single base and triangular sides (fewer faces than a prism net with 5 faces: 2 triangles + 3 rectangles).

Answer:

Question 6: (Depends on the net's diagram, but conceptually, the segment equal in length and adjacent in the folding pattern to \( A \) (e.g., the corresponding side of the adjacent triangular face) will match. If we assume a regular net, the segment with the same length as \( A \) and part of the triangle that folds to meet \( A \)'s triangle.)
Question 7: A. Right triangular prism