Question

each statement is always true. select all statements for which the converse is also always true. statement: if 2 angles form a straight angle, then they are supplementary. converse: if 2 angles are supplementary, then they form a straight angle. statement: in an isosceles triangle, the base angles are congruent. converse: if the base angles of a triangle are congruent, then the triangle is isosceles. statement: if a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. converse: if a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment. statement: if 2 angles are vertical, then they are congruent. converse: if 2 angles are congruent, then they are vertical. statement: if 2 lines are perpendicular, then they intersect to form 4 right angles. converse: if 2 lines intersect to form 4 right angles, then they are perpendicular.

Explanation:

Step1: Analyze first statement

The statement "If 2 angles form a straight - angle, then they are supplementary" is true. But the converse "If 2 angles are supplementary, then they form a straight - angle" is false because two supplementary angles can be non - adjacent.

Step2: Analyze second statement

The statement "In an isosceles triangle, the base angles are congruent" is true. The converse "If the base angles of a triangle are congruent, then the triangle is isosceles" is also true by the isosceles triangle theorem.

Step3: Analyze third statement

The statement "If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment" is true. The converse "If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment" is also true by the definition of a perpendicular bisector.

Step4: Analyze fourth statement

The statement "If 2 angles are vertical, then they are congruent" is true. But the converse "If 2 angles are congruent, then they are vertical" is false as there are many non - vertical congruent angles.

Step5: Analyze fifth statement

The statement "If 2 lines are perpendicular, then they intersect to form 4 right angles" is true. The converse "If 2 lines intersect to form 4 right angles, then they are perpendicular" is also true by the definition of perpendicular lines.

Answer:

• Statement: In an isosceles triangle, the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.
• Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
• Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles. Converse: If 2 lines intersect to form 4 right angles, then they are perpendicular.