Question

Based on the diagram, which reason justifies this statement?

If ZCEF is complementary to DC, then
ADCF = • Complements of the same angle are congruent.
O Complements of congruent angles are congruent.
O Supplements of the same angle are congruent.
- O Supplements of congruent angles are congruent.

Answer 1

ADCF and angle ZCEF are congruent because they are complementary to the same angle (angle DC), and thus ADCF = ZCEF.

Explanation:

Based on the given information, the reason that justifies the statement "If ZCEF is complementary to DC, then ADCF" is:

Complements of congruent angles are congruent.

Complementary angles are two angles that add up to 90 degrees. If ZCEF is complementary to DC, it means that the sum of the measures of angles ZCEF and DC is 90 degrees.

According to the reason stated above, if two angles are complementary to the same angle, then those two angles are congruent. Therefore, angle ADCF and angle ZCEF are congruent because they are complementary to the same angle (angle DC), and thus ADCF = ZCEF.