PROBLEM: A town planner wants to place a fountain equidistant from three trees in the park. Where should he place the fountain?

VocabularyWord Definition Diagram Notation/Name

Concurrent

Point of Concurrency

Points of ConcurrencyGUIDED NOTES

A circumcenter of a triangle can be inside, on, or outside of a triangle. No matter where, you will still be able to circumscribe the triangle. Try it on each of the triangles below.

VocabularyWord Definition Diagram

Circumcenter of a triangle

Circumscribe

VocabularyWord Definition Diagram

Incenter of a Triangle

Inscribe

If you construct angle bisectors at the three vertices of a triangle, the segments will intersect at one point. This point of concurrency where the angle bisectors intersect is known as the incenter of the triangle.

It is important to note that the incenter of a triangle will always lie inside the triangle.

The incenter is equidistant from the sides of the triangle. You can draw a circle centered on the incenter that just touches the three sides of the triangle. This is called an inscribed circle.

Try it on the triangle below!

MEDIANS1. Locate the midpoint of each side of the triangle below by constructing perpendicular bisectors. 2. Label these midpoints M1, M2 and M3.3. The MEDIAN of a triangle is a segment that connects the midpoint of a side to the opposite

vertex. In a different color, connect the three medians of the triangle using your straightedge.4. Locate and label the centroid C

**EXTRA CREDIT: The centroid in physics is referred to as the physical center of mass or the center of gravity of an object. Create a cardboard cut-out of a triangular region, locate the centroid so that the triangle could be perfectly balanced on the tip of a pencil at that point.

VocabularyWord Definition Diagram

Median of a triangle

Centroid

ALTITUDES1. Construct a perpendicular from each vertex of the triangle to its opposite side.2. Locate and label the orthocenter O.

VocabularyWord Definition Diagram

Altitude of a triangle

Orthocenter

HOW ARE WE GOING TO REMEMBER ALL THIS!?!?Develop a way – acronym, anagram, rhyme, etc. – to remember the points of concurrency and the

intersecting lines that form them.