# Proving the Congruent Supplements Theorem

Given: $\angle 1$ and $\angle 2$ are supplements, $\angle 3$ and $\angle 4$ are supplements, and $\angle 1 \cong \angle 4$. Prove: $\angle 2 \cong \angle 3$

| Statements | Reasons | |
| --- | --- | --- |
| $m \angle 1+m \angle 2=180$ | $m \angle 3+m \angle 4=180$ | $\angle 1$ and $\angle 2$ are supp. |
| $\angle 3$ and $\angle 4$ are supp. | $\angle 1 \cong \angle 4$ | $m \angle 1+m \angle 2=m \angle 3+m \angle 4$ |

Assemble the proof by dragging tiles to the Statements and Reasons columns.

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# Proving the Congruent Supplements Theorem

Given: $\angle 1$ and $\angle 2$ are supplements, $\angle 3$ and $\angle 4$ are supplements, and $\angle 1 \cong \angle 4$. Prove: $\angle 2 \cong \angle 3$

|  Statements | Reasons |   |
| --- | --- | --- |
|  $m \angle 1+m \angle 2=180$ | $m \angle 3+m \angle 4=180$ | $\angle 1$ and $\angle 2$ are supp.  |
|  $\angle 3$ and $\angle 4$ are supp. | $\angle 1 \cong \angle 4$ | $m \angle 1+m \angle 2=m \angle 3+m \angle 4$  |

Assemble the proof by dragging tiles to the Statements and Reasons columns.

StudyXY · Accepted Answer

I'll solve this proof step by step using proper LaTeX formatting: : Understand the Given Information : Define Supplementary Angles : Use the Congruence of $\angle 1$ and $\angle 4$ : Algebraic Manipulation : Rearrange the Equation : Conclusion \angle 2 \cong \angle 3$ is proven.

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I'll solve this proof step by step using proper LaTeX formatting:

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: Understand the Given Information

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