Question

Which of the following are acute scalene triangles?

Answer 1

Answer:

Y and Z.

Step-by-step explanation:

My reasoning is that because scalene triangles have all different measurements, Y and Z would be correct since they have multiple different measurements. X is an obtuse triangle, while W is a right triangle, so that leaves Y and Z.

Answer 2

Answer:  C.  Y and Z only

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Explanation:

Triangle W is a right triangle because of the square marker. This angle is 90 degrees, also known as a right angle.

Acute triangles on the other hand must have all angles smaller than 90 degrees. This rules out triangle W.

The missing angle of triangle X is 180-40-35 = 105 degrees, showing this triangle is obtuse. Obtuse triangles have exactly one angle that is between 90 and 180. Therefore, we rule out triangle X as well.

Triangles Y and Z are acute because all angles are smaller than 90 degrees. For triangle Y, the missing angle is 180-70-80 = 30. For triangle Z, the missing angle is 180-65-45 = 70 degrees.

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That takes care of the "acute" portion. Now onto the "scalene" part.

All four triangles shown are scalene. Why? Because all three sides are different lengths, as indicated by the different tickmarks.

However, we ruled out triangles W and X since they weren't acute.

Therefore, triangles Y and Z are both acute and scalene.