Maths-
Explanation :-
- alternate interior angles are supplementary
Therefore, Option A is correct
Maths-General
Explanation :-
- alternate interior angles are supplementary
Therefore, Option A is correct
- Corresponding angles are equal
- Alternate angles are equal
- Sum of the interior angles formed on one side of the transversal line is two right angles
- The Sum of the interior angles formed on one side of the transversal line is a right angle
In geometry, a transversal is a line that intersects two or more other (often parallel ) lines.
In the figure below, line n is a transversal cutting lines l and m .
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .
In the figure the pairs of corresponding angles are:
∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8
When the lines are parallel, the corresponding angles are congruent .
When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .
In the above figure, the consecutive interior angles are:
∠ 3 and ∠ 6 ∠ 4 and ∠ 5
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary .
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .
In the above figure, the alternate interior angles are:
∠ 3 and ∠ 5 ∠ 4 and ∠ 6
If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .
In the above figure, the alternate exterior angles are:
∠ 2 and ∠ 8 ∠ 1 and ∠ 7
If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent .
Example 1:
In the above diagram, the lines j and k are cut by the transversal l . The angles ∠ c and ∠ e are…
A. Corresponding Angles
B. Consecutive Interior Angles
C. Alternate Interior Angles
D. Alternate Exterior Angles
The angles ∠ c and ∠ e lie on either side of the transversal l and inside the two lines j and k .
Therefore, they are alternate interior angles.
The correct choice is C .
Example 2:
In the above figure if lines A B ↔ and C D ↔ are parallel and m ∠ A X F = 140 ° then what is the measure of ∠ C Y E ?
The angles ∠ A X F and ∠ C Y E lie on one side of the transversal E F ↔ and inside the two lines A B ↔ and C D ↔ . So, they are consecutive interior angles.
Since the lines A B ↔ and C D ↔ are parallel, by the consecutive interior angles theorem , ∠ A X F and ∠ C Y E are supplementary.
That is, m ∠ A X F + m ∠ C Y E = 180 ° .
But, m ∠ A X F = 140 ° .
Substitute and solve.
140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 °
Answer
Hint: According to the question given in the question we have to determine that the statement If two parallel lines are cut by transversal, then a pair of alternate interior angles not equal is true or false. So, first of all we have to draw two parallel lines and a transversal line which intersects the two parallel lines which is as below:
Complete step-by-step solution:
Step 1: First of all we have to draw the diagram for If two parallel lines are cut by transversal, then a pair of alternate interior angles not equal is true or false. So, first of all we have to draw two parallel lines and a transversal line which intersects the two parallel lines as mentioned in the solution hint. Hence,
Therefore option (B) is correct.
Note: If two parallel lines are intersected by another transversal line then the alternate interior angles formed are congruent or we can say equal to each other.
When a transversal cuts two lines such that pairs of alternate interior angles are , then the lines have to be parallel.
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