answer to a two column proof problem such as Given: angle 1 and angle 5 are congruent and angle 5 is congruent to angle 4 prove angle 3 is comgruent to angle 1

Given: AD,BF and CG each bisect the hexagon and meet at point H,DA,FB and HD,HF

Prove:HA,HB

To prove that angle 3 is congruent to angle 1, we can use a two-column proof. Here's an outline of the steps you can follow:

Step 1: Write down the given information in the "Given" column. In this case, write "angle 1 ≅ angle 5" and "angle 5 ≅ angle 4."

Step 2: Find a known theorem or postulate that relates the given information to the statement you want to prove. In this case, we can use the Transitive Property of Congruence, which states that if two things are congruent to the same thing, then they are congruent to each other.

Step 3: Write down the theorem or postulate that you'll apply in the "Reason" column. In this case, write "Transitive Property of Congruence."

Step 4: State the statement you want to prove in the "Statement" column. In this case, write "angle 3 ≅ angle 1."

Step 5: Write down the justification for each step of the proof. Using the Transitive Property of Congruence, we can say that if angle 1 is congruent to angle 5, and angle 5 is congruent to angle 4, then angle 1 is congruent to angle 4. Since angle 4 and angle 3 are corresponding angles, we can conclude that angle 1 is congruent to angle 3.

Here's how the two-column proof would look:

Given: angle 1 ≅ angle 5, angle 5 ≅ angle 4
Statement | Reason
------------------------------------------
angle 1 ≅ angle 5 | Given
angle 5 ≅ angle 4 | Given
angle 1 ≅ angle 4 | Transitive Property
angle 1 ≅ angle 3 | Corresponding angles

Therefore, we have proved that angle 3 is congruent to angle 1 based on the given information and the Transitive Property of Congruence.