9 questions · timed · auto-graded
If two adjacent angles are equal, then each angle measures 90°.
Angles forming a linear pair can both be acute angles.
Explanation:
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.Explanation:
The figure is given as follows:
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.Explanation:
Theoram states: If a transversal intersects two parallel lines then the pair of alternate interior angles is equal.Explanation:
Let l and m are two parallel lines. And transversal t intersects l and m making two pair of alternate interior angles, $\angle{1},\angle{2}$ and $\angle{3},\angle{4}.$
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 $\angle{3}=\angle{4}.$Explanation:
The above statement holds good if the lines are parallel only.