Given that you follow the instructions, what types of triangles do you end up with when placing the stake further down the river?
No Explanation: See solution.
Practice makes perfect
Using the instructions from example 2, we create two congruent triangles which is why we can measure the distance across the river. Specifically, since ∠ LMK and ∠ PMN are vertical angles, ∠ N and ∠ K are both right angles, and because NM≅ KM, we can by the ASA Congruence Theorem claim congruence.
If we place the stake further down the river, as long as we follow the same set of instructions, all that happens is that the vertical legs of our right triangles increases. We still end up with two congruent triangles.
Measuring the segment L'K' will, just like measuring LK, provide us with the distance across the river as these lengths are congruent corresponding sides.
