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The common mistake is you may not
know what a perpendicular bisector is.
Circumcenter Theorem
The perpendicular bisectors of the sides of a triangle intersect at a point that is equidistant from the vertices of the triangle.
Perpendicular Bisectors
A line perpendicular to a segment at the segment's midpoint.
Inscribed Circle
a circle is inscribed in a polygon if each side of the polygon is tangent to the circle.
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
Converse of the Angle BIsector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of an angle.
Centroid
The point inside the triangle that divides each median by the same ratio.
Centroid Theorem
The centroid of a triangle is located 2/3 of the distance from each vert to the midpoint of the opposite side
Orthocenter
The intersection of the lines that contain the altitudes.
Altitude
A perpendicular segment from a vertex to the line containing the opposite side.
E
F
D
27(1/3)=9
GD=9
9X2=18
AG=18
14/2=7
BG=7
16/2=8
FG=8
G
A
B
C
If AD=27, EG=14, and CG=16, find each measure
K
H
Midsegment
A line segment that connects the midpoints of two sides of the triangle.
Triangle Midsegment Theorem
The segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of that side.
I
Find the measure of <HIK given that <HIJ equals 120 degrees.
IK s an angle bisector.
120/2=60
<HIK=60
<IJK=60
J