Question

omar is constructing equilateral triangle abc. he needs to copy $overline{ab}$ to form the other two sides of the triangle. he sets the compass width to $ab$ and draws two arcs from $a$ as shown. after plotting point $c$, he will draw three line segments to connect points $a$, $b$, and $c$. what steps should he follow to plot point $c$? a) increase the compass width, draw an arc from $b$, and plot point $c$ on the new arc. b) without changing the compass width, draw an arc from $b$, and plot point $c$ on the new arc. c) increase the compass width, draw an arc from $b$ to intersect the other arc, and plot point $c$. d) without changing the compass width, draw an arc from $b$ to intersect the other arc, and plot point $c$.

Explanation:

Step1: Recall equilateral - triangle property

In an equilateral triangle, all sides are equal. So, \(AB = BC=AC\).

Step2: Analyze compass - usage for construction

Since the compass is already set to the length of \(AB\) (used to draw arcs from \(A\)), to find point \(C\) such that \(BC = AB\), we need to keep the compass width as \(AB\) (without changing it) and draw an arc from \(B\). The intersection of the arc drawn from \(B\) and the arc drawn from \(A\) will be point \(C\).

Answer:

D. Without changing the compass width, draw an arc from \(B\) to intersect the other arc, and plot point \(C\)