3.7 Constructing Points of Concurrency - Investigation 1: Concurrence
Right Triangle - Angle Bisector
It is concurrent.
Angle Measures: 23.2 degrees.
21.15 degrees.
45.66 degrees.
Obtuse Triangle - Angle Bisector
It is concurrent.
Angle Measures: 11.7 degrees.
67.86 degrees.
10.44 degrees.
Acute Triangle - Angle Bisector
It is conccurent.
Angle Measures: They are all 30 degrees.
Angle Bisector Concurrency Conjecture
The three angle bisectors of a triangle are concurrent
Right Triangle - Perpendicular Bisector
Obtuse Triangle - Perpendicular Bisector
Acute Triangle - Perpendicular Bisector
Perpendicular Bisector Concurrency Conjecture
The three perpendicular bisectors of a triangle are concurrent.
Right Triangle - Altitude
Obutuse Triangle - Altitude
Acute Triangle - Altitude
Altitude Concurrency Conjecture
The three altitudes (or the lines containing the altitudes) of a triangle are conccurent.
Step 7 - Question
In acute, right and obtuse triangles, the point of concurrency of the medians (perpendicular bisector) is inside the triangle.