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Part 2: Use congruency theorems to prove congruency. 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. Given: M ≅ X N ≅ Y YO ≅ NZ Prove: △MNO ≅ △XYZ NEED A GOOD EXPLAINATION PARAGRAPH

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cooperbrown81

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

Given

Given

Given

Definition of congruent line segments

Symmetric property of congruence

Addition and substitution properties of equality*

Segment addition theorem

Definition of congruent line segments

AAS congruence postulate

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* 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.

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