Question

True or false?

1. Two lines perpendicular to a third line must be parallel.
2. In a plane two lines perpendicular to a third line must be parallel.
3. In a plane two lines parallel to a third line must be parallel.
4. Any two lines parallel to a third line must be parallel.

Short answer

1. The provided statement is false.
2. The provided statement is true.
3. The provided statement is true.
4. The provided statement is true.

Step-by-step solution

Part a. Step 1. Make the required figures.

Make the figures that represent the provided information.

Part a. Step 2. Make an observation from the figures.

The first figure represents the perpendicular relation between of the line 1 and line 2 with the third line which are present in space but in second figure the line 1 and line 2 are not having the parallel relation between them which are present in plane.

Part a. Step 3. Make the conclusion.

According to the observation, the provided statement does not represent a true statement.

Part b. Step 1. Make the required figure.

Make the figure that represents the provided information.

Part b. Step 2. Make an observation from the figures.

The figure represents a parallel relation between line 1 and line 2 which are present in a plane.

Part b. Step 3. Make the conclusion.

According to the observation, the provided statement represents a true statement.

Part c. Step 1. Make the required figure.

Make the figure that represents the provided information.

Part c. Step 2. Make an observation from the figures.

The figure represents three lines that are having a parallel relation between them and these lines are present in a plane.

Part c. Step 3. Make the conclusion.

According to the observation, the provided statement represents a true statement.

Part d. Step 1. Make the required figure.

Make the figure that represents the provided information.

Part d. Step 2. Make an observation from the figures.

The figure represents three lines that are having a parallel relation between them.

Part d. Step 3. Make the conclusion.

According to the observation, the provided statement represents a true statement.