Final answer:
The converse that is false is the one for Statement B, which states that if two angles are congruent, then they are right angles. This is false because congruent angles can have any measure and are not limited to being right angles.
Step-by-step explanation:
You asked for which of the given statements the converse is false. The converse of a statement is made by switching the hypothesis and conclusion of the statement. We will examine each statement and its converse.
- Statement A: If two parallel lines are intersected by a transversal, then the corresponding angles are congruent. Converse: If the corresponding angles are congruent when two lines are intersected by a transversal, then the two lines are parallel. This is true by the Converse of the Corresponding Angles Postulate.
- Statement B: If two angles are right angles, then they are congruent. Converse: If two angles are congruent, then they are right angles. The converse is false because congruent angles can have any measure, not just 90 degrees.
- Statement C: If a triangle is equilateral, then all of the sides of the triangle are congruent. Converse: If all of the sides of a triangle are congruent, then the triangle is equilateral. This converse is true because a triangle with all congruent sides is by definition equilateral.
- Statement D: If a ray bisects an angle, then it divides the angle into two congruent angles. Converse: If an angle is divided into two congruent angles by a ray, then the ray bisects the angle. This converse is true as the definition of angle bisector implies the angles are congruent.
Therefore, the converse that is false is that of Statement B: If two angles are congruent, then they are right angles.