Geometry problems involving triangle congruence and angle properties.
Understand the Problem
The image contains multiple-choice geometry questions. The questions involve concepts like triangle congruence, properties of angles, and types of triangles based on their sides. We need to identify the specific geometric principles being tested and select the correct choices.
Answer
$$\angle G \cong \angle O$$
Answer for screen readers
$$\angle G \cong \angle O$$
Steps to Solve
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Identify Given Information We know from the problem that $\overline{GT} \cong \overline{OM}$ and $\overline{GM} \cong \overline{OT}$.
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Apply the Reflexive Property of Congruence By the reflexive property, we can state that $\overline{MT} \cong \overline{MT}$.
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Establish Triangle Congruence Since we have two sides and the included side being the same, the triangles are congruent using the SSS (Side-Side-Side) congruence theorem.
Therefore, we can state: $$\triangle GTM \cong \triangle OMT$$
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Conclude Corresponding Angles Are Congruent From the congruence of triangles, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we conclude that: $$\angle G \cong \angle O$$
$$\angle G \cong \angle O$$
More Information
The angles $\angle G$ and $\angle O$ are congruent because the triangles $\triangle GTM$ and $\triangle OMT$ are proven to be congruent by the SSS congruence theorem.
Tips
- Confusing Triangle Congruence Criteria: Make sure to correctly apply the right theorem. Always check if the conditions for SSS, SAS, or AAS are met.
- Forgetting CPCTC: After proving triangle congruence, it's common to forget to state that corresponding angles are congruent.
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