Question

adam makes several statements after he observes the diagram above, which has the following properties: a, b, c, and d are collinear. b is the mid - point of ac. c is the mid - point of bd. identify the statements as theorems, conjectures, or axioms. statement: ab = 1/2ac. there is only one line that can be drawn connecting the points. ab + bc+cd = ad. theorem, conjecture, or axiom: select select select select

Explanation:

Step1: Analyze the first - statement "AB = 1/2AC"

Since B is the mid - point of AC, by the definition of a mid - point, the length of AB is half of the length of AC. This is a well - known geometric property and is an axiom (a basic, self - evident truth in geometry).

Step2: Analyze the second statement "There is only one line that can be drawn connecting the points"

This is the line - segment postulate in geometry, which is an axiom. It states that for any two distinct points, there is exactly one line segment that connects them.

Step3: Analyze the third statement "AB + BC+CD = AD"

Since A, B, C, and D are collinear, by the segment addition postulate (an axiom in geometry), the sum of the lengths of non - overlapping segments on the same line equals the length of the entire segment.

Step4: Analyze the fourth statement "3AB = AD"

This is a conjecture. We do not have enough information from the given mid - point and collinearity facts to prove it as a theorem. It is a statement that seems to be a guess based on the figure but has not been proven.

Answer:

Axiom, Axiom, Axiom, Conjecture