Question

1. determine whether the statement is true or false based on the diagram alone: ( ab ) is perpendicular to plane ( s ) a. true b. false 5. determine whether the statement is true or false based on the diagram alone: ( cd ) is perpendicular to plane ( t ) a. true b. false

Explanation:

Step1: Recall the definition of a line perpendicular to a plane

A line is perpendicular to a plane if it is perpendicular to every line in the plane that it intersects.

Step2: Analyze line \(AB\) and plane \(S\)

From the diagram, \(AB\) is perpendicular to the intersection line of plane \(T\) and plane \(S\), but there is no indication that \(AB\) is perpendicular to every line in plane \(S\). So the statement “\(AB\) is perpendicular to plane \(S\)” is false.

Step3: Analyze line \(CD\) and plane \(T\)

Line \(CD\) lies in plane \(S\). There is no indication that \(CD\) is perpendicular to plane \(T\). In fact, \(CD\) is not perpendicular to the intersection line of plane \(T\) and plane \(S\) (which is a key - line for checking perpendicularity between a line and a plane). So the statement “\(CD\) is perpendicular to plane \(T\)” is false.

Answer:

1. B. False
2. B. False