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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1. We know from the problem that there is a side of length

8\ \text{cm}

and two angles:

45^\circ

and

80^\circ

.
2. The total sum of internal angles of a triangle is

180^\circ

. Therefore, the remaining angle in each triangle is:

180^\circ - 45^\circ - 80^\circ = 55^\circ

3. This gives us a unique set of angles:

45^\circ, 80^\circ, 55^\circ

in each triangle.
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

8\ \text{cm}

and we have no information about the lengths of the other sides, the triangles might not be congruent.

Final Answer: The triangles are not necessarily congruent.

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