State if the two triangles are congruent. If they are, state how you know.
Understand the Problem
The question is asking whether the two triangles shown are congruent and requires reasoning based on specific congruence criteria (SSS, SAS, ASA).
Answer
Yes, they are congruent by ASA.
Answer for screen readers
Yes, they are congruent by ASA.
Steps to Solve
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Identify Corresponding Parts Compare the two triangles to see if there are congruent sides or angles marked or indicated. In this case, there are two angles that appear to be the same (marked by arcs) in both triangles.
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Check Congruence Criteria Since we have information about two angles in both triangles, we can apply the Angle-Side-Angle (ASA) postulate. This states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent.
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State the Congruence Since we established that two angles are congruent and assume the side between them is congruent as well, we conclude that the triangles are congruent by ASA.
Yes, they are congruent by ASA.
More Information
The ASA postulate is a fundamental theorem in geometry used to prove triangle congruence. It helps simplify the comparison of triangles by focusing on their angles and the included side.
Tips
- Assuming SSS without verifying sides: Students often assume all sides are congruent without checking. Always verify by comparing parts directly.
- Mistaking angle types: Ensure that the marked angles are indeed the ones being discussed. Mislabeling angles can lead to incorrect conclusions about congruence.
