Question
Preeti told Pavani that if the alternate interior angles are equal then lines need not be parallel. Is Preeti's statement true or false?
Answer: Option B
:
B
If two parallel lines are intersected by a transversal:
(i) alternate interior angles are equal i.e., ∠2=∠8 and ∠3=∠5
(ii) alternate exterior angles are equal i.e., ∠1=∠7 and ∠4=∠6
(iii) corresponding angles are equal i.e., ∠1=∠5,∠4=∠8,∠2=∠6 and ∠3=∠7
(iv) co-interior angles are supplementary i.e., ∠2 +∠5= 180∘and∠3 +∠8 =180∘.
Hence, if the alternate angles are equal then the lines are parallel.
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:
B
If two parallel lines are intersected by a transversal:
(i) alternate interior angles are equal i.e., ∠2=∠8 and ∠3=∠5
(ii) alternate exterior angles are equal i.e., ∠1=∠7 and ∠4=∠6
(iii) corresponding angles are equal i.e., ∠1=∠5,∠4=∠8,∠2=∠6 and ∠3=∠7
(iv) co-interior angles are supplementary i.e., ∠2 +∠5= 180∘and∠3 +∠8 =180∘.
Hence, if the alternate angles are equal then the lines are parallel.
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