Relationships within TrianglesChapter 55.1 Midsegment Theorem
and Coordinate ProofMidsegment of a Triangle- a segment that
connects the midpoints of 2 sides of a triangle.
Midsegment TheoremThe segment connecting the midpoints of 2
sides of a triangle is parallel to the 3rd side and is half as long
as that side.
Coordinate ProofPlace geometric figures in a coordinate planeUse
variables to represent the coordinates of the figure
Coordinate Proof of Midsegment Theorem
ExampleGraph OHJ. O(0,0) H(m,n) J(m,0) Is OHJ a right triangle?
Find the lengths of the sides and the coordinates of each
midpoint.
5.2 Use Perpendicular BisectorsPerpendicular Bisector
Theorem
Perpendicular Bisector Converse
ExampleFind x.
ExampleThree forest ranger stations are the same distance from
the main office. How would you find the location of the main
office?
5.3 Use Angle BisectorsAngle Bisector Theorem
Angle Bisector Converse
ExampleFind x so that P lies on the bisector of 16, then x <
-4Given:Prove:
