Question

write the converse of the statement below. then determine whether the statement is true or false. If false, give a counterexample. Conditional Statement: If 2 angles are corresponding in parallel lines, then they are congruent.

Answer 1

Answer:

Converse statement is ''If two angles are congruent, then they are corresponding angles in parallel lines''.

The converse statement is false.

Step-by-step explanation:

Statement is ''If 2 angles are corresponding in parallel lines, then they are congruent.''

Converse statement is ''If two angles are congruent, then they are corresponding angles in parallel lines''.

Consider the figure.

Here,

$l||m$

As ∠1 and ∠2 are alternate interior angles,

∠1 ≅ ∠2

(if two lines are parallel then each pair of alternate interior angles is equal)

So, ∠1 ≅ ∠2 but ∠1 and ∠2 are alternate interior angles not corresponding angles.

The converse statement is false.