Question

1. proof complete the two - column proof. then write a flowchart proof. (see example 2.) given ∠abd is a right angle. ∠cbe is a right angle. prove ∠abc≅∠dbe statements reasons 1. ∠abd is a right angle. ∠cbe is a right angle. 1. ______ 2. ∠abc and ∠cbd are complementary. 2. definition of complementary angles 3. ∠dbe and ∠cbd are complementary. 3. ____ 4. ∠abc≅∠dbe 4. ____ 19. proving a theorem complete the paragraph proof for the congruent complements theorem. then write a two - column proof. (see example 3.) given ∠1 and ∠2 are complementary. ∠1 and ∠3 are complementary. prove ∠2≅∠3 ∠1 and ∠2 are complementary, and ∠1 and ∠3 are complementary. by the definition of ____ angles, m∠1 + m∠2 = 90° and ____ = 90°. by the ____, m∠1 + m∠2 = m∠1 + m∠3. by the subtraction property of equality, ______ so, ∠2≅∠3 by the definition of

Explanation:

Step1: Given information

Given that $\angle ABD$ is a right - angle and $\angle CBE$ is a right - angle.

Step2: Complementary angles property for $\angle ABC$ and $\angle CBD$

Since $\angle ABD = 90^{\circ}$, and $\angle ABD=\angle ABC+\angle CBD$, by the definition of complementary angles (two angles whose sum is $90^{\circ}$), $\angle ABC$ and $\angle CBD$ are complementary.

Step3: Complementary angles property for $\angle DBE$ and $\angle CBD$

Since $\angle CBE = 90^{\circ}$, and $\angle CBE=\angle DBE+\angle CBD$, by the definition of complementary angles, $\angle DBE$ and $\angle CBD$ are complementary.

Step4: Congruence of $\angle ABC$ and $\angle DBE$

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:

1. Given
2. Definition of complementary angles
3. Complements of the same angle are congruent