Question

Adam, a construction manager in a nearby town, needs to check the uniformity of Yield signs around the state and is checking the heights (altitudes) of the Yield signs in your locale. Adam knows that all yield signs have the shape of an equilateral triangle. Why is it sufficient for him to check just the heights (altitudes) of the signs to verify uniformity?​

Answer 1

Adam can check the uniformity of Yield signs by measuring their altitudes because all sides and angles in an equilateral triangle are equal, meaning the height determines the size of all other dimensions.

Step-by-step explanation:

Adam, the construction manager, checks the heights (altitudes) of Yield signs to verify uniformity because all Yield signs are in the shape of an equilateral triangle. In an equilateral triangle, all sides have the same length and all angles are equal, 60 degrees each. Thus, the height is directly proportional to the side length. Verifying the altitude of these signs is sufficient because if the altitude is uniform across all signs, the base and the angles will also be uniform due to the properties of equilateral triangles.

This principle is similar to using the Pythagorean Theorem where measurements are consistent and reliable. Just as the theorem consistently gives correct outcomes when applied correctly, the measurement of the height of equilateral triangles will consistently give information about their overall size and uniformity.