Question 11 Mark
The following statements are true (T) and which are false (F)? Give reasons.
Two lines perpendicular to the same line are perpendicular to each other.
Two lines perpendicular to the same line are perpendicular to each other.
Answer
View full question & answer→FalseExplanation:
The figure can be drawn as follows:
Here, $\text{l}\perp\text{n}$ and $\text{m}\perp\text{n}$ It is given that $\text{l}\perp\text{n},$ therefore, $\angle{1}=90^\circ\dots(\text{i})$ Similarly, we have $\text{m}\perp\text{n},$ therefore, $\angle{2}=90^\circ\dots(\text{ii})$ From (i) and (ii), we get: $\angle{1}=\angle{2}$ But these are the pair of corresponding angles. Theorem states: If a transversal intersects two lines in such a way that a pair of correspondung angles is equal, then the two lines are parallel. Thus, we can say that l || m.
The figure can be drawn as follows:
Here, $\text{l}\perp\text{n}$ and $\text{m}\perp\text{n}$ It is given that $\text{l}\perp\text{n},$ therefore, $\angle{1}=90^\circ\dots(\text{i})$ Similarly, we have $\text{m}\perp\text{n},$ therefore, $\angle{2}=90^\circ\dots(\text{ii})$ From (i) and (ii), we get: $\angle{1}=\angle{2}$ But these are the pair of corresponding angles. Theorem states: If a transversal intersects two lines in such a way that a pair of correspondung angles is equal, then the two lines are parallel. Thus, we can say that l || m.
We need to prove that $\angle{1}=\angle{2}$ and $\angle{3}=\angle{4}.$ We have, $\angle{2}=\angle{5}$ [Vertically opposite angles] Again, $\angle{3}=\angle{6}$ [Corresponding angles] Hence, $\angle{1}=\angle{2}$ and $\angle{3}=\angle{4}.$
It is given that l || m and m || n We need to show that l || m We have l || m, thus, corresponding angles should be equal. That is, $\angle{1}=\angle{2}$ Similarly, $\angle{3}=\angle{2}$ Therefore, $\angle{1}=\angle{3}$ But these are the pair of corresponding angles. Therefore, l || m.