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When there are two parallel lines cut by a transversal, which of the following is true? a) Corresponding angles are equal. b) Alternate interior angles are supplementary. c) Consecutive angles on the same side of the transversal are equal. d) Alternate interior angles are equal.
Only a
b and c
a and d
Only b
a and d
Remember that all 'alternate' and 'corresponding' angle pairs formed by parallel lines and a transversal are equal, while consecutive interior angles sum to 180°.
Two parallel lines cut by a transversal.
Corresponding angles=Equal,Alternate interior angles=Equal,Consecutive interior angles=Supplementary
Remember that all 'alternate' and 'corresponding' angle pairs formed by parallel lines and a transversal are equal, while consecutive interior angles sum to 180°.
Confusing consecutive interior angles (which are supplementary, summing to 180°) with alternate interior angles (which are equal).
Analyze the properties of parallel lines
When two parallel lines are intersected by a transversal line, several angle relationships are formed.
m∥n,t is transversal
Evaluate Option (a): Corresponding angles
Corresponding angles occupy the same relative position at each intersection, and they are always equal when lines are parallel.
Corresponding angles=Equal
Evaluate Option (d): Alternate interior angles
Alternate interior angles lie on opposite sides of the transversal and between the two parallel lines. They are always equal.
Alternate interior angles=Equal
Conclusion
Both option a and option d state correct properties of parallel lines cut by a transversal. Therefore, a and d are both true.
Both (a) and (d) are correct
C is correct because both corresponding angles (Option a) and alternate interior angles (Option d) are equal when two parallel lines are cut by a transversal.
In coordinate geometry, parallel lines have identical slopes, which directly corresponds to equal angles formed with a shared transversal line.
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