Question

question 1 2 pts when constructing an equilateral triangle, what is the purpose of setting the compass to the same length as the segment? to create arcs (part of a circle) from each endpoint with radius = segment length. to measure the degrees (around the circle) from each endpoint of the segment. to create an arc from one endpoint to the other (a semi - circle) then connecting the points of intersection. to look pretty. question 2 2 pts when constructing the angle bisector, why must we create arcs on the angles legs first? creating arcs in the interior of the angle from any point on the legs is also acceptable. the interior intersection points must be equidistant from the legs. it adds a circular degree measure to the bisector by creating sets of circular arcs. it allows us to demonstrate correct use of the compass. question 3 2 pts when constructing the perpendicular segment bisector, why is it important to have the compass adjusted longer than the midpoint? if it were less than the midpoint, the segment wouldnt be perpendicular. if it were less than the midpoint, the semicircles wouldnt intersect. its not really important, the compass can be set at any length, it just needs to make a circle centered at each endpoint. its important to create an equilateral triangle.

Explanation:

Question 1

When constructing an equilateral triangle, setting the compass to the same length as the segment is to create arcs from each endpoint. The radius of these arcs is equal to the segment length. This is a fundamental step in the geometric construction of an equilateral triangle. The intersection of these arcs gives the third vertex of the equilateral triangle.

When constructing an angle bisector, creating arcs on the angle's legs first is necessary. The interior intersection points of these arcs (and subsequent arcs) must be equidistant from the legs of the angle. By the property of angle bisectors (a point on the bisector is equidistant from the sides of the angle), this ensures that the line drawn through the vertex and the intersection of the arcs is the angle bisector.

When constructing a perpendicular segment bisector, if the compass length were less than the mid - point (half of the segment length), the semicircles (or arcs) centered at each endpoint would not intersect. Intersection of these arcs (drawn with radius greater than half of the segment length) is required to find the two points that lie on the perpendicular bisector.

Answer:

To create arcs (part of a circle) from each endpoint with radius = segment length.

Question 2