Question
Alex and Heather each draw a triiangle with one side of 8cm, one angle of 45°and one angle of 80°. Alex says that their triangles are congruent. Explain why Alex might not be correct
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Answer to a math question Alex and Heather each draw a triiangle with one side of 8cm, one angle of 45°and one angle of 80°. Alex says that their triangles are congruent. Explain why Alex might not be correct
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4.697 Answers
1. We know from the problem that there is a side of length 8\ \text{cm} 45^\circ 80^\circ
2. The total sum of internal angles of a triangle is180^\circ
180^\circ - 45^\circ - 80^\circ = 55^\circ
3. This gives us a unique set of angles:45^\circ, 80^\circ, 55^\circ
4. Since the corresponding angles in both triangles are equivalent, the triangles fall under the Angle-Angle-Angle (AAA) similarity criterion.
5. However, AAA similarity does not guarantee that the triangles are congruent. Congruence requires that the corresponding sides are congruent.
6. Because only one side of both triangles is given as8\ \text{cm}
Final Answer: The triangles are not necessarily congruent.
2. The total sum of internal angles of a triangle is
3. This gives us a unique set of angles:
4. Since the corresponding angles in both triangles are equivalent, the triangles fall under the Angle-Angle-Angle (AAA) similarity criterion.
5. However, AAA similarity does not guarantee that the triangles are congruent. Congruence requires that the corresponding sides are congruent.
6. Because only one side of both triangles is given as
Final Answer: The triangles are not necessarily congruent.
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