Theorem. Example. Centroid Theorem. The centroid of a triangle is located. 2. 3 of the distance from ... â BAH m. ______ by CPCTC. D. Equilateral â...
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Geometry Notes Section 5-3 Medians and Altitudes of Triangles AH, BJ, and CG are medians of a triangle. They each join a vertex and the midpoint of the opposite side.
The point of intersection of the medians is called the centroid of ∆ABC.
Theorem
Centroid Theorem The centroid of a triangle is 2 located of the distance from 3 each vertex to the midpoint of the opposite side.
Example
Given: AH, CG, and BJ are medians of nABC. 2 2 2 Conclusion: AN AH, CN CG, BN BJ 3 3 3
In QRS, RX 48 and QW 30. Find each length. 1. RW
2. WX
3. QZ
4. WZ
JD, KE, and LC are altitudes of a triangle. They are perpendicular segments that join a vertex and the line containing the side opposite the vertex.
The point of intersection of the altitudes is called the orthocenter of ∆JKL.
Fun facts about medians, altitudes, and angle bisectors ! Isosceles ∆ABC with AB = AC. Draw altitude AH from vertex angle A to base BC .
A
B
C
AH is also a median and angle bisector.
Why? Triangle ABH is congruent to ∆_______ by ________. Therefore, BH = ______ and mBAH __________ by CPCTC.
Equilateral ∆DEF Draw altitudes DX , EY , and FZ . Each altitude is also a median and angle bisector of ∆DEF.
