Question

Writing a Two-Column Proof Thy It Angles Reasons Given: ZABC ZDEF and ZGHI ZDEF Prove: MZABC = mZGHI ZABC ZDEF LGHI M_ABC 2GHI

Answer 1

By using a two-column proof structure, it is shown that if ∠ABC is congruent to ∠DEF and ∠GHI is congruent to ∠DEF, then m∠ABC must equal m∠GHI due to the transitive property of equality.

Step-by-step explanation:

To prove that m∠ABC equals m∠GHI, we will follow a two-column proof structure:

1. 
   
3. Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF.
4. 
   
6. ∠ABC is congruent to ∠DEF (Given).
7. 
   
9. ∠GHI is congruent to ∠DEF (Given).
10. 
    
12. If two angles are congruent, then their measures are equal (Definition of Congruent Angles).
13. 
    
15. Therefore, m∠ABC = m∠DEF (From Step 2 and 4).
16. 
    
18. Similarly, m∠GHI = m∠DEF (From Step 3 and 4).
19. 
    
21. If m∠ABC = m∠DEF and m∠GHI = m∠DEF, then m∠ABC = m∠GHI (Transitive Property of Equality).

Hence, we have proved that the measure of angle ABC is equal to the measure of angle GHI.