Question
Complete using one of the choices below: If two planes have two common points
𝐴 and 𝐵, then they ______.
- Intersect at a straight line parallel to line AB
- Intersect at line AB
- Have a third point in common, which does not belong to line AB
- Are coincident
Hint:
We know that two planes are intersecting if they are not parallel and they always intersect a straight line. Also, we know that exactly one particular straight line can pass through two given points. So, if two planes have two common points, then they must be intersecting and the line at which they intersect will be the line passing through that two common points.
Therefore, if the two planes have two common points 𝐴 and 𝐵, then they intersect at line AB.
The correct answer is: Intersect at line AB
To find if two planes have two common points A and B then how they will intersect with each other.
Note that if two given planes intersect, then they always intersect at a straight line.
Therefore, if the two planes have two common points 𝐴 and 𝐵, then they intersect at line AB.
Related Questions to study
What does it mean for two lines to be considered skew?
Note that two lines that lie on two different planes may also be parallel.
What does it mean for two lines to be considered skew?
Note that two lines that lie on two different planes may also be parallel.
Which of the following statements is true about the two planes?
Which of the following statements is true about the two planes?
Read the following conditional statement: If Siddharth does his homework, then he gets his weekly allowance.
What is the conclusion?
Note that a conditional statement is not always in the form "If-then", for example, "All natural numbers are integers". This is a conditional statement but not in the form of "If-then". But it can be rewritten in the form "If-then" as follows: "If a number is a natural number, then it is an integer."
Read the following conditional statement: If Siddharth does his homework, then he gets his weekly allowance.
What is the conclusion?
Note that a conditional statement is not always in the form "If-then", for example, "All natural numbers are integers". This is a conditional statement but not in the form of "If-then". But it can be rewritten in the form "If-then" as follows: "If a number is a natural number, then it is an integer."
Read the following conditional statement: If Siddharth does his homework, then he gets his weekly allowance.
What is the hypothesis?
If the statement is in the form “if A, then B” then here A is the hypothesis and B is the conclusion.
Read the following conditional statement: If Siddharth does his homework, then he gets his weekly allowance.
What is the hypothesis?
If the statement is in the form “if A, then B” then here A is the hypothesis and B is the conclusion.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the contrapositive of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the contrapositive of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the inverse of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the inverse of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the converse of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the converse of the statement.
If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.
Look at the pattern 2, 4, 6, 8, 10, ...
What is the 19th term in the pattern?
We observed that there is a difference of two in each case and then found the no corresponding to 19th position = 38
Look at the pattern 2, 4, 6, 8, 10, ...
What is the 19th term in the pattern?
We observed that there is a difference of two in each case and then found the no corresponding to 19th position = 38
A dot pattern is shown below. What would the total number of dots be in the 6th figure?
In the solution first we observed all the images and then based on the feedback we got we found no of dots in 6th image = 21 dots
A dot pattern is shown below. What would the total number of dots be in the 6th figure?
In the solution first we observed all the images and then based on the feedback we got we found no of dots in 6th image = 21 dots
Find a pattern for the sequence. Use the pattern to find the next three terms in the sequence.
2, 4, 7, 11,...
In this question first we found how the pattern is there and we observed it is based on the difference so we found difference in each case and obtained the continuing terms of the series.
Find a pattern for the sequence. Use the pattern to find the next three terms in the sequence.
2, 4, 7, 11,...
In this question first we found how the pattern is there and we observed it is based on the difference so we found difference in each case and obtained the continuing terms of the series.
Which box is next in the sequence?
Which box is next in the sequence?
Which box is next in the sequence?
Which box is next in the sequence?
Which box is next in the sequence?
Which box is next in the sequence?
The measure of 
is ____________.
Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is 
and sum of two consecutive angles is 
. The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.
The measure of is ____________.
Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is and sum of two consecutive angles is . The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.
The value of x is _________.
Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is and sum of two consecutive angles is . The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.
The value of x is _________.
Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is and sum of two consecutive angles is . The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.
