Question

The figure shown is a rectangular prism. Which edges are perpendicular to PR¯¯¯¯¯? Select each correct answer. Responses TR¯¯¯¯¯ segment T R QT¯¯¯¯¯ segment Q T TJ¯¯¯¯¯ segment T J HP¯¯¯¯¯¯ segment H P RA¯¯¯¯¯ segment R A rectangular prims. vertices in the front clockwise from top left are t, r, a, j. vertices in the back clockwise from top left are q, p, h, e.

Answer 1

`\sf A)\quad \overline{\sf TR}`

`\sf D)\quad \overline{\sf HP}`

`\sf E)\quad \overline{\sf RA}`

Explanation:

A rectangular prism is a three-dimensional geometric solid with six rectangular faces, twelve edges, and eight vertices (corners).

Each edge connects two vertices and is shared by two adjacent faces.

Opposite edges are parallel and have the same length because the prism is rectangular.

Adjacent edges are perpendicular because all the angles within a rectangular prism are right angles.

The edge
`\overline{\sf PR}` is the edge connecting vertex P and vertex R.

To find the edges that are perpendicular to
`\overline{\sf PR}`, we need to identify the edges that share a common vertex with either P or R and are perpendicular to
`\overline{\sf PR}`.

Edges that share a vertex with P:

• 
  `\overline{\sf PR}`
• 
  `\overline{\sf HP}`
• 
  `\overline{\sf PQ}`

Edges that share a vertex with R:

• 
  `\overline{\sf PR}`
• 
  `\overline{\sf TR}`
• 
  `\overline{\sf RA}`

Out of these edges, the edges that are perpendicular to
`\overline{\sf PR}` are:

• 
  `\overline{\sf RA}`
• 
  `\overline{\sf HP}`
• 
  `\overline{\sf TR}`