Question

1. Error Analysis Your classmate says you can use the Triangle-Angle-Bisector Theorem to find the value of x in the diagram. Explain what is wrong with your classmate's statement.

Answer 1

Triangle-Angle-Bisector Theorem : An angle bisector is a straight line drawn from the vertex of a triangle to its opposite side in such a way, that it divides the angle into two equal or congruent angles in such a way that the ratio of the two line-segments is proportional to the ratio of the other two sides.

In the given triangle FIH, line IG is divide the angle I

So, from the defination of angle bisector theorem : The ratio of two line segments is proportional to the ratio of the other two sides.i.e.

$\frac{IF}{FG}=\frac{IH}{HG}$

In the given figure : IF = x,