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Mathematics Experiment #2

Triangle Area Experiment

Given triangle ABC and point P not on line AB, AC, or BC. The point where line PA intersects line BC is X. The point where line PB intersects line AC is Y. The point where line PC intersects line AB is Z. 

Measure each of the indicated segments and place your results in the following table. Draw 9 more triangles of various types (right, obtuse, acute, scalene, isosceles, equilateral), and repeat the experiment. Do you see any pattern?

Triangle #
AZ
ZB
BX
XC
CY
YA
1
2
3
4
5
6
7
8
9
10