Geometry Chapter 5 Summary sections 1 - 4
Know and use the distance formula
Formula:
Find the distance from (4, -2) to (6, 7)
Know and use the midpoint formula
Formula:
Find the midpoint between (4, -2) and (6, 7)
The three main characteristics of midsegments of triangles
1.
2.
3.
How do we prove segments parallel?
How do we prove one segment is half the length of another segment?
The two main characteristics of a perpendicular bisector
1.
2.
How do we prove segments perpendicular?
How do we prove a segment is bisected?
The Perpendicular Bisector Theorem
And its Converse
The Angle Bisector Theorem
And its Converse
How do we find points on the perpendicular bisector of a segment?
Ex. Find two points on the perpendicular bisector of AB if A(2, 1) and B(3, 6)
Concurrent means
Perpendicular bisectors of the sides of a triangle are segments that
1.
2.
Circumscribed circle
Circumcenter
Where is the circumcenter of
An acute triangle?
An obtuse triangle?
A right triangle?
Carefully sketch examples of each
How do you find the circumcenter of a triangle if you only know the coordinates of the vertices?
Bisectors of the angles of a triangle are rays that
1.
2.
Incenter
Inscribed circle
How do you find the incenter of a triangle?
Draw a triangle and carefully sketch its incenter
Median of a triangle is a segment
From:
To:
The medians of a triangle are concurrent at a point
Centroid
Altitude of a triangle
Median
Points of concurrency in triangles:
Circumcenter :
Concurrency point of the:
Where does it occur with respect to the triangle?
Special characteristics:
Incenter:
Concurrency point of the:
Where does it occur with respect to the triangle?
Special characteristics:
Orthocenter :
Concurrency point of the:
Where does it occur with respect to the triangle?
Special characteristics:
Centroid :
Concurrency point of the:
Where does it occur with respect to the triangle?
Special characteristics: