To Prove : The Ceva's Theorem for the given conditions.
Explanation of Solution
Given information:
If P is any point inside
Construct ?ABC with points Y, Z, and X on sides BC, AC, and AB, respectively.
Let the concurrent line segments be AY, BZ and CX.
The point of intersection is point P.
Construct line I through C parallel to line AB and extend segments AY and BZ to meet I at points G and H, respectively.
Since
Since they are alternate interior
Similarly
Hence, triangles
By the same reasoning, the following pairs of similar triangles
From the first similarity,
Hence. Ceva's theorem is proved.
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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