A group of students on a hiking trip wants to find the distance AB across a pond (see the following figure). One student suggests choosing any point C, connecting it with B, and then finding point D such that <DCB ≅ <ACB and DC≅AC. How and why does this help in finding the distance AB?
ppl cant help you with the answer b/c you didn't show us the diagram
The method suggested by the student involves constructing a triangle using point C, and then finding a point D such that angle DCB is congruent to angle ACB and side DC is congruent to side AC.
By doing this, the student is essentially creating a congruent triangle to triangle ACB. Congruent triangles have the same shape and size, so the triangles ACB and DCB can be overlapped perfectly.
Now, since the triangles are congruent and AB is a side of triangle ACB, there must be a corresponding side on triangle DCB that is congruent to AB. In this case, side DB corresponds to side AB.
Therefore, by measuring or calculating the length of side DB, which was constructed to be congruent to side AC, we can determine the length of side AB.