Question

Two intersecting lines will form how many pairs of congruent angles?

Answer 1

Hint: To solve this question first we need to recall the definition of congruent angles. Then we will draw two lines intersecting each other and observe how many congruent angles will be formed to get the desired answer.

Complete step by step answer:
We have to find the number of pairs of congruent angles formed when two lines intersect.
We know that congruent angles are angles with exactly the same measurement i.e. equal to each other.
We know that vertical angles are angles which are opposite to each other and formed by two intersecting lines.
Now, according to the vertical angle theorem, when we draw two lines intersecting each other than the vertical (opposite) angles will always be congruent.
So if we draw two lines intersecting each other we get two pairs of congruent angles.

In the above diagram AB and CD two lines intersecting each other then we will get
$\mathrm{\angle }1=\mathrm{\angle }2\text{ and }\mathrm{\angle }3=\mathrm{\angle }4$
Hence we get two pairs of congruent angles.

Note:
Generally we get two pairs of congruent angles when two lines intersect. If two lines are intersecting and perpendicular to each other than all four angles will be congruent because they are right angles.

In the above diagram AB and CD are two lines intersecting each other and perpendicular to each other. So the angles formed are right angles and congruent to each other.
Here $\mathrm{\angle }AED=\mathrm{\angle }BEC=\mathrm{\angle }BED=\mathrm{\angle }AEC=90{}^{\circ }$