Question

Which of the following statements is true in its conditional and converse forms?

If K is between points J and L, then K is a midpoint.
If a polygon has 3 sides, then the sum of its interior angles is 180°.
If two angles are right angles, then they are congruent.
If B is the midpoint of AC¯¯¯¯¯¯¯¯, then AB = BC.

Answer 1

The converse statement involves switching the hypothesis and the conclusion of a conditional statement.

The correct statement is (d) If B is the midpoint of AC, then AB = BC.

The converse of the given conditional statements are:

• If K is a midpoint, then K is between points J and L
• If the sum of interior angles is  180°, then the polygon has 3 sides
• If two angles are congruent, then they are right angles
• If AB = BC, then B is the midpoint of AC

From the above statements, (a), (b) and (c) are not the same as the conditional statement, because:

• Point K does not have to be between points J and L to be a midpoint.
• The sum of interior angles of all polygons (whether it has 3 sides or more) is 180 degrees
• Congruent angles may not be right angles

For option (d):

For B to be a midpoint of AC, it means that sides AB and BC are congruent.

Hence, the correct statement is (d)

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