If hexagon A is similar to hexagon B and hexagon B is similar to hexagon C, then what conclusion can be drawn? What property does this illustrate?
If hexagon A is similar to hexagon B and hexagon B is similar to hexagon C, then the conclusion that can be drawn is that hexagon A is similar to hexagon C. This is known as the transitive property of similarity.
To understand why this conclusion can be made, it's important to first understand what it means for two polygons to be similar. Two polygons are considered similar if their corresponding angles are congruent and the ratios of their corresponding side lengths are equal.
So, if hexagon A is similar to hexagon B, it means that the angles of hexagon A are congruent to the corresponding angles of hexagon B, and the side lengths of hexagon A have the same ratios as the corresponding side lengths of hexagon B.
Similarly, if hexagon B is similar to hexagon C, it means that the angles of hexagon B are congruent to the corresponding angles of hexagon C, and the side lengths of hexagon B have the same ratios as the corresponding side lengths of hexagon C.
By the transitive property, since hexagon A is similar to hexagon B and hexagon B is similar to hexagon C, it follows that hexagon A is also similar to hexagon C.
This property of similarity is a fundamental concept in geometry and is used to establish relationships between different figures based on their corresponding angles and side ratios.