Geometry
Notes – Lesson 5.3
Name _______________________________
Part I – Special segments of triangles
Three or more lines intersecting in a point are __________________________
The point of intersection is called the _________________ of __________________________.
I. Altitude of a triangle is the __________________ segment from _______________________ to
_____________________.
The point of concurrency is called the ________________________ of the triangle.
II. Median of a triangle is the segment from ______________________
to _______________________of __________________________
The point of concurrency is called the ___________________ and
always lies inside the triangle.
III. Perpendicular Bisector of a triangle are the segments that are _______________
_______________ of each side of the triangle
Theorem 5-6: The point of concurrency is called the ______________________ of
the triangle and is ___________________ from the vertices.
A circle can be circumscribed about the triangle using the circumcenter as the center.
With your compass, construct the circumscribed circle on the diagram at the right.
IV. Bisectors of the angles of a triangle are the segments that
________________________________.
Theorem 5-7: The point of concurrency is called the ______________________
of the triangle and is _______________________ from the sides.
A circle can be inscribed in the triangle using the incenter of the triangle as the
center and the distance to the sides as the radius.
Use your compass to trace the inscribed circle in the diagram at the right.
Part II. Constructing Inscribed and Circumscribed circles.
1. Construct the angle bisectors and use the point of concurrency to
construct inscribed circle
2. Find the center of the circle that circumscribes
the triangle and construct the circle.
Part III. Examples
Problems 3-8: Is
an altitude, median, perpendicular bisector, or angle bisector of the triangle?
3.
6.
4.
7.
9.
10. City Planners plan to place a drinking fountain equidistant from the
tennis court, playground, and volleyball court. How would they place
it?
5.
8.