Page 5: Practical Applications of Geometric Theorems

The final page applies geometric theorems to real-world scenarios, particularly focusing on emergency response planning.

Example: The fire hydrant problem demonstrates how the perpendicular bisector theorem can be used to determine optimal emergency response positions.

Highlight: The perpendicular bisector theorem has practical applications in determining equal-distance points from two fixed locations.

Page 1: Triangle Theorems and Problem-Solving Fundamentals

This page introduces fundamental triangle congruence theorems and their applications through practical problems. The content covers finding segment lengths using algebraic methods and geometric theorems.

Definition: The centroid of a triangle is the point where all three medians intersect, dividing each median in a 2:1 ratio.

Example: Problem 3 demonstrates the application of the Centroid Theorem where BP = 13 and the solution requires finding LP and BL using the 2:3 ratio.

Highlight: The Perpendicular Bisector Theorem and its converse are crucial for solving problems involving equal distances from a point to endpoints of a segment.

Vocabulary: Incenter - The point where the angle bisectors of a triangle intersect.