Question

do you understand? 1. essential question how is inductive reasoning used to recognize mathematical relationships? 2. error analysis esteban made the following drawing and then stated this conjecture: “the altitude of a triangle always lies inside of or along the side of the triangle.” what error did esteban make?

Explanation:

Step1: Recall definition of triangle altitude

The altitude of a triangle is a line segment from a vertex perpendicular to the opposite - side.

Step2: Consider different types of triangles

In an obtuse - angled triangle, the altitude from the vertex of the obtuse angle lies outside the triangle.

Step3: Analyze Esteban's statement

Esteban's statement is wrong because he did not consider obtuse - angled triangles.

Answer:

Esteban did not consider obtuse - angled triangles. In an obtuse - angled triangle, the altitude from the vertex of the obtuse angle lies outside the triangle, so the altitude of a triangle does not always lie inside of or along the side of the triangle.