Question

1. construct an isosceles triangle using mn as its base and legs that are congruent to rs as shown. leave all construction marks. n m r s

Explanation:

Step1: Draw arcs from endpoints

Using a compass, set the width to the length of $\overline{RS}$. Place the compass at point $N$ and draw an arc above $\overline{MN}$. Then place the compass at point $M$ and draw an arc of the same radius (length of $\overline{RS}$) above $\overline{MN}$.

Step2: Mark intersection and connect

The two arcs drawn in Step 1 will intersect at a point (let's call it $P$). Connect point $P$ to point $N$ and point $P$ to point $M$.

Answer:

The isosceles triangle $\triangle MNP$ is constructed where $\overline{MN}$ is the base and $\overline{NP}=\overline{MP}=\overline{RS}$.