Question

5 from unit 1, lesson 4 this diagram is a straightedge and compass construction. which triangle is equilateral? explain how you know.

Explanation:

Step1: Recall equilateral - triangle property

An equilateral triangle has all sides equal. In straight - edge and compass construction, equal - length segments are often created by using the same radius of circles.

Step2: Analyze the blue triangle $\triangle VZW$

In the given straight - edge and compass construction, the circles centered at $V$, $Z$, and $W$ intersect at the vertices of the blue triangle $\triangle VZW$. The radii of these circles are used to form the sides of the triangle. Since the distance between any two of the points $V$, $Z$, and $W$ is equal to the radius of the circles used in the construction, $VZ = ZW=WV$.

Step3: Analyze the red triangle $\triangle STU$

The sides of the red triangle $\triangle STU$ do not seem to be formed by the same - length radii of the circles in the construction. So, we cannot say that $ST = TU = US$.

Answer:

The blue triangle $\triangle VZW$ is equilateral because its sides are formed by the radii of the circles in the straight - edge and compass construction, making all its sides equal in length.