Question

When two parallel lines are transected by the two intersecting lines then the two triangles so formed are

• A. Congruent to each other
• B. Similar to each other
• C. Right angled triangles
• D. None

Answer 1

The correct option is B Similar to each other

When two parallel lines are cut by the two intersecting lines the two triangles will always be similar to each other.
let us see by the diagram, there are two possibilities
one is,in this figure,
$\angle A$ is common in both triangles and $\angle ABC=\angle ADE\text{(corresponding angles)}$
So triangles are similar.

And one possibility is,
In this figure also,
$\angle DAE=\angle CAB\left(\text{vertically opposite angles}\right)$
$\angle ADE=\angle ACB\left(\text{alternate angles}\right)$
Hence, triangles are similar.

So, option$\left(b\right)$ correct.