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Chapter 3: Q12 (page 86)

Reword Theorem 3-8 as two statements, one describing existence and the other describing uniqueness.

Short Answer

Expert verified

The existence is that “a parallel line to another line consists of a point that is positioned on outer area of another line”. The uniqueness is that “the count of line is one that is parallel to another line also it consist of a point that is positioned on outer area of another line”.

Step by step solution

01

Step 1. Definition of theorem 3-8

Theorem 3-8 states that a parallel line to another line consist of a point that is positioned on outer area of another line.

02

Step 2. Split the theorem in existence and uniqueness

The theorem 3-8 consists of existence that “a parallel line to another line consists of a point that is positioned on outer area of another line”.

The theorem 3-8 consists of uniqueness that “the count of line is one that is parallel to another line also it consist of a point that is positioned on outer area of another line”.

03

Step 3. Make the conclusion

As the obtained existence and uniqueness completes the theorem so these are the required existence and uniqueness.

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