Q10. - Geometry

Question

Given the diagram, tell whether you can reach the conclusion shown.

Which postulate justifies the statement $AX+XC=AC$?

Step-by-Step Solution

Answer

The segment addition postulate is the required postulate.

Step 1. Find the suitable postulate.

The postulate 2 is the suitable postulate which states that if a point with the name of $X$ is present between 2 points with the name of $Y$ and $Z$ these points are the end points of a line then it should satisfy the equation:

$YX+XZ=YZ$

Step 2. Relate the postulate.

According to the given figure the point $Y$ is same as the point $A$ and the point $Z$ is same as the point $C$ because the point $X$ is just in the middle of the points $A$ and $C$ also these two points are the end point of a line.

Step 3. Make the conclusion by using the relation.

As the provided equation is according to the segment addition postulate so the required postulate is segment addition postulate.