Question

Alex and Heather each draw a triangle 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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Darrell

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1. Identify the given information:

- One side: 8 \, \text{cm}

- One angle: 45^\circ

- One angle: 80^\circ

2. Calculate the third angle in each triangle because the sum of angles in a triangle is 180°:

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

3. Construct the triangles:

- One triangle might have the side of 8cm between the 45^\circ and 80^\circ angles.

- Another triangle might have the side of 8cm opposite one of these angles.

4. Conclude that having the same two angles and a side does not ensure congruence unless the position of the side relative to the angles is specified.

So, the triangles might not be congruent.

- One side:

- One angle:

- One angle:

2. Calculate the third angle in each triangle because the sum of angles in a triangle is 180°:

3. Construct the triangles:

- One triangle might have the side of 8cm between the

- Another triangle might have the side of 8cm opposite one of these angles.

4. Conclude that having the same two angles and a side does not ensure congruence unless the position of the side relative to the angles is specified.

So, the triangles might not be congruent.

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