Question

three friends want to meet at a place that is the same distance from each of their houses. they draw a map and measure the approximate distances and angles, as shown. which step should they take next to find a meeting place that is the same distance from each persons house? find the midpoint of the segments which connect their houses. bisect each of the angles with vertices at their houses. draw perpendicular lines through any point on the segments which connect their houses. draw perpendicular line segments from each vertex to the opposite side. jos house 38° 0.5 miles 0.6 miles 88° boriss house 0.4 miles 54° carries house

Explanation:

Step1: Recall geometric concept

The point that is equidistant from the vertices of a triangle is the circum - center. The circum - center is found by constructing the perpendicular bisectors of the sides of the triangle.

Step2: Analyze each option

• Finding the mid - point of the segments connecting their houses just gives the mid - points of the sides, not the equidistant point.
• Bisecting the angles gives the in - center which is equidistant from the sides of the triangle, not the vertices.
• Drawing perpendicular lines through any point on the segments is not the correct method.
• Drawing perpendicular bisectors of the sides (which is equivalent to drawing perpendicular line segments from the mid - point of each side to the side) will help find the circum - center. Among the options, the closest to constructing perpendicular bisectors is to draw perpendicular line segments from each vertex to the opposite side (in an isosceles or equilateral triangle, the altitude, median and perpendicular bisector coincide, and in general, this is related to the process of finding the circum - center).

Answer:

Draw perpendicular line segments from each vertex to the opposite side.