Question

if ∠a and ∠b are complementary and ∠a and ∠c are complementary, then ∠b≅∠c. this is a(n) dropdown statement. i can dropdown by using dropdown.

Explanation:

Step1: Recall definition of complementary angles

Complementary angles add up to 90 degrees. So, $\angle A+\angle B = 90^{\circ}$ and $\angle A+\angle C=90^{\circ}$.

Step2: Solve for $\angle B$ and $\angle C$

From $\angle A+\angle B = 90^{\circ}$, we get $\angle B=90^{\circ}-\angle A$. From $\angle A+\angle C = 90^{\circ}$, we get $\angle C=90^{\circ}-\angle A$.

Step3: Compare $\angle B$ and $\angle C$

Since $\angle B = 90^{\circ}-\angle A$ and $\angle C=90^{\circ}-\angle A$, then $\angle B\cong\angle C$. This is a true statement and can be proven by the transitive - property of equality (or the congruent - complements theorem).

Answer:

This is a(n) true statement. I can prove it by using the congruent - complements theorem (or the transitive property of equality).