Question

(PLEASE!!!!) The congruency of MNO and XYZ can be proven using a reflection across the line bisecting OZ. However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Answer 1

Hello! I had this same question on a test, so I am going to share the answers that I were told are 100% correct!

1: Given

2: Given

3: Given

4: Definition of congruence

5: Reflexive Property

6: Addition property

7: Segment addition postulate

8: Definition of congruence

9: AAS Congruency theorem

Of course, some tests are worded differently, so some extra reading is required. However, I hope this helps, good luck! :)

Answer 2

Explanation:

Only the reasons need be given here, as the statements are already given in your figure.

1. Given
2. Given
3. Given
4. Definition of congruent line segments
5. Symmetric property of congruence
6. Addition and substitution properties of equality*
7. Segment addition theorem
8. Definition of congruent line segments
9. AAS congruence postulate

_____

* The addition property says if A=B, then A+C=B+C. The substitution property further says if C=D, then A+C=B+D (D can be substituted for C). IMO, both properties are needed together to get from A=B and C=D to A+B=C+D.