Question

Consider the following figure. H C K 73° A M Q Jazeel used the above diagram to conclude that IM = CQ. Explain the rationale behind Jazeel's conclusion and justify whether or not his conclusion is correct.

Answer 1

Rationale behind Jazeel's conclusion: since two sides of ΔHAM and ΔCKQ are congruent, then the third side of both triangles will be congruent.

Jazeel's conclusion is NOT CORRECT because the angles opposite each of the third side of both triangles are not equal, the third sides cannot be congruent.

What are Congruent Triangles?

• Triangles that are congruent to each other are said to be triangles having pairs of angles and sides that are equal to each other.
• All the corresponding parts of two congruent triangles must be equal.

Thus, Jazeel's assumed that since two sides of ΔHAM and ΔCKQ are congruent, then the third side of both triangles will be congruent.

Jazeel's conclusion is NOT CORRECT because the angles opposite each of the third side of both triangles are not equal. Therefore, the third sides cannot be congruent.

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