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Module 8: Bisectors and Medians of Triangles

The common mistake is you may not

know what a perpendicular bisector is.

Vocabulary 8.1

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.

Vocabulary 8.2

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.

Vocabulary 8.3

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.

By Caroline Hampton and Tyler Stallings

8.3 Problem

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

8.2 Problem

K

H

Vocabulary 8.4

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

Thank You!

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