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3.4 Medians, Altitudes & (Slightly) More Complex Proofs

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Presentation on theme: "3.4 Medians, Altitudes & (Slightly) More Complex Proofs"— Presentation transcript:

1 3.4 Medians, Altitudes & (Slightly) More Complex Proofs

2 Medians Definition: A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. Median Midpoint

3 Three Medians per Triangle

4 Altitudes Definition: An altitude of a triangle is a segment drawn from the vertex of a triangle perpendicular to the (line containing) the opposite side. Can be inside, on a side, or outside the triangle Acute Triangle: Altitude inside Right Triangle: Altitude is a side Obtuse Triangle: Altitude outside

5 THREE ALTITUDES PER TRIANGLE

6 Altitude - Special Segment of Triangle
In a right triangle, two of the altitudes of are the legs of the triangle. B A D F B A D F I K In an obtuse triangle, two of the altitudes are outside of the triangle.

7 Two Points Determine a Line
Postulate: The Line Postulate Two Points Determine a Line (or line segment) Abbreviated: LP

8 Auxiliary Lines Additional lines needed, NOT drawn in the given diagram. A Given: Prove : Easily proven if we had triangles, but we don’t. B Or do we? Any two points determine a line (or segment) D C Now triangles are congruent by SSS and angles are congruent by CPCTC

9 Write the proof now in 2 columns
Given: Prove : A When you introduce a line segment into a diagram write: Statement Reason Let Line Postulate (LP) B D C

10 Identifying Medians and Altitudes
Is KX a median, an altitude, neither, or both? Both

11 Homework Help

12


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