Question

Using the information in the map, what is the distance between Camden and Lowell? Explain your reasoning using correct Geometry justification. For the ease of symbols used in your justification, let Morsetown be point o, Meridian be point M, Grenata be point G, Camden be

point C, and Lowell be point L.

The map below shows five different towns. The town of Meridian wasgiven its name because it lies exactly halfway between two pairs of cities:
Camden and Grenata, and Lowell and Morsetown.

Answer 1

5 miles

Explanation:

We are looking at triangles LCM and OGM.

Point M is the midpoint of segments LO and CG.

That makes segments CM and GM congruent (side).

Then angles CML and GMO are congruent since they are vertical angles (angle).

Finally, segments LM and OM are also congruent because of the midpoint (side).

By SAS, triangles LCM and OGM are congruent.

Then by CPCTC, segments LC and OG are congruent.

Since OG = 5 miles, then LC = 5 miles.

Answer: 5 miles