Q5 - Geometry

Question

Postulate 6 is sometimes stated as “Two points determine a line.”

 

Do two intersecting lines determine a plane?

Step-by-Step Solution

Answer

Yes, two intersecting lines determine a plane.

Step 1. State postulate 6.

Postulate 6 states that “Two points determine a line”.

Step 2. State Theorem 1-3.

Theorem 1-3 is stated as “If two lines intersect, then exactly one plane contains both the lines.”.

Step 3. Significance of theorem 1-3.

From the above theorem, it is clear that only one plane is there which can contain both the intersecting lines. It can be depicted by the diagram below.

So, it can be said that two intersecting lines determine a plane.