Question

What general rule can be derived from the following sequence using inductive reasoning?

A. Every triangle is divided in half each time
B. Every triangle is rotated each time
C. Every triangle is divided into 4 triangles each time
D. Every triangle gets smaller each time

Answer 1

Inductive reasoning involves making generalizations from observations, such as deducing a pattern of division within a sequence of triangles. This contrasts with deductive reasoning, which starts with a known rule to determine specifics.

Step-by-step explanation:

The question is asking for the use of inductive reasoning to derive a general rule from a sequence of changes applied to a triangle in a geometric pattern. Inductive reasoning involves making generalizations based on specific observations. In the sequence provided, we are to determine whether the triangle gets divided, rotated, made smaller, or divided into a specific number of smaller triangles each time. An example of inductive reasoning would be seeing a pattern where each triangle is divided into a certain number of smaller triangles. For instance, if we observe that every step in the sequence results in each triangle being split into four smaller triangles, we might conclude that 'Every triangle is divided into 4 triangles each time.'

Similarly, deductive reasoning, which is drawing a conclusion based on general rules or premises, would be like knowing the properties of a triangle (three sides, sum of angles equals 180 degrees) and concluding something specific about a particular triangle. For example, if we know one angle measure, we can deduce the possible range of the other two angles.