Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 3: Q4. (page 82)
For each statement
- tell whether the statement is true or false,
- write the converse,
- tell whether the converse is true or false.
Two planes are parallel only if they do not intersect.
Short Answer
- Given statement is true
- Two planes do not intersect only if they are parallel.
- Converse statement is true.
Step by step solution
Part a. Step 1. Meaning of Parallel lines.
A plane can be considered to be consisted of several parallel lines lying in the plane.
As it is clear from the figure that line A and Line B are parallel to each other, and they are not intersected.
Part a. Step 2. Meaning of given statement.
When two planes do not intersect each other then they are parallel
Part a. Step 3. Conclusion.
From first and second statement given statement is true.
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�
Part b. Step 2. Find P and Q in given statement.
P is 鈥淧lanes do not intersect鈥�
Q is 鈥淧lane are parallel鈥�
Part b. Step 3. Converse of given statement.
Two planes do not intersect only if they are parallel.
Part c. Step 1. Meaning of non-intersecting planes.
Consider that the two planes do not intersect. So, the angle between the two planes must be either 0 or 180 degrees.
If planes are considered to be consisted of several parallel lines, the angle between the lines of two planes will also be either 0 or 180 degrees.
That means, the lines of one plane are parallel to the lines of the other planes. This implies that the planes are parallel.
Part c. Step 2. Meaning of converse statement.
When two planes are parallel then they do not intersect
Part c. Step 3. Conclusion.
From step 1 and 2 converse statement is true.
Over 30 million students worldwide already upgrade their learning with 91影视!
