Two Column Geometric Proofs

Question

Hello. I have a question about a two column proof. It is given that angle 1 and angle 2 are congruent to each other. We have to prove that angle 3 and angle 4 are congruent.  For reference, look at this pic: https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A89fb8b8a5aa864a14a464e21a0fa066585c3c96906204da16c699504%2BIMAGE%2BIMAGE.1

Answer 1

STEP 1:  ANGLE 1 = ANGLE 2    GIVEN. Note I just type = because it's easier, PLUS there is nothing else about angles being congruent other than the fact that their measurements are the same.

 

STEP 2:  ANGLE 1 IS EQUAL TO ANGLE 3    VERTICAL ANGLES ARE EQUAL.

 

STEP 3:  ANGLE 1 = ANGLE 2 = ANGLE 3    Transitive property of equality, combining steps 1 & 2 (quantities equal to a third quantity are equal to each other).

 

STEP 4:  ANGLE 2 = ANGLE 4      VERTICAL ANGLES ARE EQUAL.

 

STEP 5:  ANGLE 3 = ANGLE 4      Because each of these equals ANGLE 2 (TRANSITIVE PROPERTY OF =, see steps 3 & 4)

 

Q. E. D.