Question

for exercises 3-5, use $overline{pq}$. 3. explain how you can use point q to find point r such that $angle rpq$ is a copy of $angle g$.

Explanation:

1. First, place the compass on point \(G\) of \(\angle G\) and draw an arc that intersects both rays of \(\angle G\), say at points \(M\) and \(N\).
2. Then, without changing the compass - width, place the compass on point \(Q\) of \(\overrightarrow{PQ}\) and draw an arc that intersects \(\overrightarrow{PQ}\), say at point \(S\).
3. Next, measure the distance between \(M\) and \(N\) with the compass.
4. Then, with the compass width set to the distance \(MN\), place the compass on point \(S\) and draw an arc that intersects the previously - drawn arc (from step 2), say at point \(R\). The point \(R\) is such that \(\angle RPQ\) is a copy of \(\angle G\) because we have used the compass to transfer the angle - measure by creating congruent triangles (by the SSS - Side - Side - Side congruence criterion for the triangles formed by the arcs and the rays).

Answer:

Follow the steps: 1. Arc on \(\angle G\). 2. Arc on \(\overrightarrow{PQ}\). 3. Measure \(MN\). 4. Intersect arcs to find \(R\).