Question

tyler claims that if two triangles each have a side length of 11 units and a side length of 8 units, and also an angle measuring , they must be identical to each other. Do you agree? Explain your reasoning.

Answer 1

Answer: Yes I agree, they must be identical to each other.

Step-by-step explanation: One of the conditions based on which triangles are similar is the SSA criteria, that is, Side-Side-Angle.

According to Tyler, two sides have been measured as 11 units and 8 units respectively in both triangles. If the corresponding angle is the same as indicated in the question, then the third side must be the same measurement. However, if the angles are of different sizes, then the third side would also be different for both triangles. For instance if the angle in triangle A is wider than that of triangle B, then the third side in triangle A would be longer than that of triangle B and in that case they would not be similar. Also if the angle in triangle A is narrower than that of triangle B, then the third side of triangle A would be shorter than that of triangle B and both triangles would not be similar as well.

Please refer to the picture attached. In the upper part of the picture, triangle A and triangle B are not similar though they both have sides measuring 11 and 8 units because angle x is not equal to angle y. However in the lower part, both triangles A and B are equal because both have angle x and sides 11 and 8 units, and that makes the third side have the same measurement.