Question

1. conditional: if two parallel lines are cut by a transversal, then alternate interior angles are congruent. write the converse: valid or invalid: counterexample: if ∠x = 44°, then ∠y = what is the angle relationship between x and y? if ∠x = 119°, then ∠y = what is the angle relationship between x and y?

Explanation:

1. Analyze the angle - relationship in the first part

Given $\angle x = 44^{\circ}$, assume the two parallel lines are cut by a transversal. If $\angle x$ and $\angle y$ are alternate - interior angles (by the property of parallel lines cut by a transversal), then $\angle y=\angle x$. So $\angle y = 44^{\circ}$. The relationship between $\angle x$ and $\angle y$ is that they are alternate - interior angles.

2. Analyze the angle - relationship in the second part

Given $\angle x = 119^{\circ}$, if the two lines are parallel and cut by a transversal, and $\angle x$ and $\angle y$ are alternate - interior angles, then $\angle y=\angle x$. So $\angle y = 119^{\circ}$. The relationship between $\angle x$ and $\angle y$ is that they are alternate - interior angles.

3. Find the converse of the conditional statement

The conditional statement is: If two parallel lines are cut by a transversal, then alternate - interior angles are congruent.
The converse of a conditional statement "If $p$, then $q$" is "If $q$, then $p$". So the converse is: If alternate - interior angles are congruent, then two parallel lines are cut by a transversal.
This converse is valid. There is no counter - example because if alternate - interior angles are congruent, then the lines must be parallel (by the converse of the alternate - interior angles theorem).

Answer:

1. If $\angle x = 44^{\circ}$, then $\angle y = 44^{\circ}$, relationship: alternate - interior angles
2. If $\angle x = 119^{\circ}$, then $\angle y = 119^{\circ}$, relationship: alternate - interior angles
3. Converse: If alternate - interior angles are congruent, then two parallel lines are cut by a transversal.

Valid or Invalid: Valid
Counterexample: None