Question

∠dbe and ∠cbd are complementary. ∠abc and ∠cbd are complementary. ∠abc≅∠cbd. ∠abc≅∠dbe. ∠cbe is a right angle. given. ∠abd is a right angle. given. definition of complementary angles. definition of complementary angles. congruent complements theorem. definition of supplementary angles. transitive property. complete a flowchart proof.

Explanation:

Step1: Recall right - angle property

Since $\angle CBE$ is a right angle, $\angle CBE = 90^{\circ}$. And since $\angle ABD$ is a right angle, $\angle ABD=90^{\circ}$.

Step2: Define complementary angles

We know that $\angle DBE+\angle CBD = 90^{\circ}$ (because $\angle CBE = 90^{\circ}$ and $\angle CBE=\angle DBE + \angle CBD$), so $\angle DBE$ and $\angle CBD$ are complementary. Also, $\angle ABC+\angle CBD = 90^{\circ}$ (because $\angle ABD = 90^{\circ}$ and $\angle ABD=\angle ABC+\angle CBD$), so $\angle ABC$ and $\angle CBD$ are complementary.

Step3: Apply congruent - complements theorem

If two angles are complementary to the same angle, then they are congruent. Since $\angle ABC$ and $\angle DBE$ are both complementary to $\angle CBD$, we have $\angle ABC\cong\angle DBE$.

Answer:

The flowchart proof is completed by using the definitions of right - angles, complementary angles and the congruent - complements theorem to show that $\angle ABC\cong\angle DBE$.