Question

2. Given: RS and ST share endpoint S. Critique the reasoning of others. Based on this information, Michaela says that the Segment Addition Postulate justifies the statement that RS + ST = RT. Is there a flaw in Michaela's reasoning, or is she correct? Explain. TAL​

Answer 1

There is a slight flaw. She is only correct if all three points are on the same line.

If S is on segment RT, then segment RT can be broken up into RS and ST. Through the segment addition postulate, we can then say

RS+ST = RT

So put another way, Michaela's claim is only true if angle RST is 180 degrees.

However, if angle RST is some other angle, then saying RS+ST = RT is not correct. So Michaela needs to clarify that point S is on segment RT. Or she could say that all three points are on the same straight line.

A diagram is provided below.

Side note: in the figure on the right, RS+ST adds up to something larger than RT. This is due to the triangle inequality theorem. That theorem states that adding any two sides of a triangle adds to something larger than the third remaining side.