Question

Select all the conditionals that have a true converse.

• A. If a quadrilateral is a square, then it has four congruent sides.
• B. If a polygon is a triangle, then it has $3$ sides.
• C. If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
• D. If two angles are congruent, then they have the same measure.
• E. If two angles are complimentary, then the sum of the measures of the angles is $90$.

Answer 1

Answer: (B), (D), (E)

If two angles are complimentary, then the sum of the measures of the angles is $90$.

Explanation for the correct options.

Option (B):

If a polygon is a triangle, then it has $3$ sides is a true statement also the converse of this statement is true as the three-sided polygon is called a triangle.

Option (D):

If two angles are congruent, then they have the same measure is a true statement and its converse is also true as angles of equal measures are congruent also.

Option (E):

If two angles are complementary, then the sum of the measures of the angles is $90°$ is a true statement as if angles whose sum is $90°$ are complementary angles.

Explanation for the incorrect options.

Option (A):

If a quadrilateral is a square, then it has four congruent sides is true but the converse of this statement is not true as rhombus also have four congruent sides.

Option (C):

If a quadrilateral is a rectangle, then it has two pairs of parallel sides is a true statement but its converse is not true as parallelograms also have two pairs of parallel sides.

Hence, options (B),(D), and (E) are correct.