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Chapter 3: Q2. (page 82)

For each statement

  1. tell whether the statement is true or false,
  2. write the converse,
  3. tell whether the converse is true or false.

If two lines are parallel, then they are not skew.

Short Answer

Expert verified
  1. Given statement is true
  2. If two lines are not skew, then they are parallel
  3. Converse statement is false.

Step by step solution

01

Part a. Step 1. Meaning of parallel and skew lines.

Lines that keep a fixed minimum distance and do not intersect are said to be parallel.

Lines that are neither intersecting nor parallel are skew lines.

02

Part a. Step 2. Meaning of given statement.

As per the definition of skew lines, as the lines are parallel, they are not skew.

03

Part a. Step 3. Conclusion.

From first and second statement given statement is true.

04

Part b. Step 1. Converse of a statement. 

Converse of a statement 鈥渋f P then Q鈥� is 鈥渋f Q then P鈥�

05

Part b. Step 2. Find P and Q in given statement.

Pis 鈥減arallel鈥�

Qis 鈥渘ot skew鈥�

06

Part b. Step 3. Converse of given statement.

If two lines are not skew, then they are parallel

07

Part c. Step 1. Meaning of skew and parallel lines.

Lines that keep a fixed minimum distance and do not intersect are said to be parallel.

Lines that are neither intersecting nor parallel are skew lines.

08

Part c. Step 2. Meaning of converse statement.

If two lines are not skew then they can be either intersecting or parallel.

09

Part c. Step 3. Conclusion.

It鈥檚 not necessary that if two lines are not skew, then they are parallel only. They can be intersecting also.

So, the converse statement is false.

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