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Q: What is the converse statement of if two parallel lines are cut by a transverse then the alternate angles are congruent?

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Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.

An obverse statement is logically equivalent.

Switching the hypothesis and conclusion of a conditional statement.

Find the converse of the following statement. If it's a dime, then it's a coin.

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If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel.

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A biconditional is the conjunction of a conditional statement and its converse.

A biconditional is the conjunction of a conditional statement and its converse.

The converse statement for 'If it is your birthday, then it is September' would be 'If it is September, then it is my birthday.'

Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.

The isosceles triangle theorem states that if two sides of a triangle are congruent, the angles opposite of them are congruent. The converse of this theorem states that if two angles of a triangle are congruent, the sides that are opposite of them are congruent.

If two line segments are congruent then they have the same length.

A simple example of a conditional statement is: If a function is differentiable, then it is continuous. An example of a converse is: Original Statement: If a number is even, then it is divisible by 2. Converse Statement: If a number is divisible by 2, then it is even. Keep in mind though, that the converse of a statement is not always true! For example: Original Statement: A triangle is a polygon. Converse Statement: A polygon is a triangle. (Clearly this last statement is not true, for example a square is a polygon, but it is certainly not a triangle!)

a converse is an if-then statement in which the hypothesis and the conclusion are switched.

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