QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# 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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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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