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Step 1:I'll solve this proof step by step using proper LaTeX formatting:
Step 2:: Understand the Given Information
- $$\angle 1 \cong \angle 4
- \angle 3 and \angle 4 are supplements
Step 3:: Define Supplementary Angles
- $$m\angle 3 + m\angle 4 = 180°
- Supplementary angles are two angles that sum to 180°
Step 4:: Use the Congruence of \angle 1 and \angle 4
- Since $$\angle 1 \cong \angle 4$$, their measures are equal
- m\angle 1 = m\angle 4
Step 5:: Algebraic Manipulation
- $$m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4
- m\angle 1 + m\angle 2 = 180°
Step 6:: Rearrange the Equation
- $$m\angle 2 = m\angle 3
- Substitute m\angle 1 = m\angle 4
Step 7:: Conclusion
- Since their measures are equal, $$\angle 2 \cong \angle 3
Final Answer
\angle 2 \cong \angle 3 is proven.
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