Sign in
Please select an account to continue using cracku.in
↓ →
Which of the following statements are true?<br>Statement I - If two lines are parallel to a third line, then they themselves are parallel.<br>Statement II - All the eight angles made by a transversal with two parallel lines are always equal.<br>Statement III - If the alternate angles made by a transversal with a pair of lines are $$80^\circ$$ and $$100^\circ$$, then the lines are parallel.<br>Statement IV - If the lines are parallel, then the interior angles on the same side of the transversal are supplementary.
Lines parallel to the same line are parallel to each other, so Statement I is true. The eight angles are not all equal; they form two groups of equal angles that add up to $$180^\circ$$, so Statement II is false. Lines are parallel only when alternate angles are equal, and $$80^\circ \neq 100^\circ$$, so Statement III is false, while Statement IV is a standard property of parallel lines and is true. Hence only I and IV are true.
Was this solution helpful?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
91- 6303239042
