Question

similarly, you can prove the congruent complements theorem.
congruent complements theorem
if two angles are complementary to the same angle (or to congruent angles), then they are congruent.
if ∠4 and ∠5 are complementary and ∠6 and ∠5 are complementary, then ∠4 ≅ ∠6.
once a theorem is proven, it can be used in subsequent proofs. the proven theorem is then a tool or strategy that helps in proving a new statement.
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try this video for extra example 2 – writing flow chart proofs

1. use the reasons bank (and the given statements) to complete the two - column proof. then write a flowchart proof.

reasons bank: congruent supplements theorem, given
given: ∠1 and ∠2 are supplementary. ∠1 and ∠3 are supplementary.
prove: ∠2 ≅ ∠3
two - column proof

statements	reasons
2.	2. given
3. ∠2 ≅ ∠3	3.

flowchart proof
1.

1. ∠1 and ∠3 are supplementary.

3.

Explanation:

Step1: Fill first reason (Given)

Statement 1 is given, so Reason 1 = Given

Step2: Fill second statement (Given)

The second given statement is $\angle 1$ and $\angle 3$ are supplementary.

Step3: Fill final reason (Theorem)

Use Congruent Supplements Theorem for the conclusion.

Two-Column Proof

STATEMENTS	REASONS
2. $\angle 1$ and $\angle 3$ are supplementary.	2. Given
3. $\angle 2 \cong \angle 3$	3. Congruent Supplements Theorem

Flowchart Proof

1. $\boldsymbol{\angle 1}$ and $\boldsymbol{\angle 2}$ are supplementary.

• Reason: Given

1. $\boldsymbol{\angle 1}$ and $\boldsymbol{\angle 3}$ are supplementary.

• Reason: Given

1. $\boldsymbol{\angle 2 \cong \angle 3}$

• Reason: Congruent Supplements Theorem

(Flowchart structure: The first two boxes both point to the third box, with their respective reasons below each box)

Answer:

Completed two-column proof and flowchart proof as shown above.