Points representing the length if a rectangle are located at A(0,0) and B(8,0). The width of the rectangle is one half its lengt
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The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.
<h3>What is the Angle Bisector Theorem?</h3>
The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.
Note that the angle that has been dissected here is ∠CBD. Thus,
=
See the link below for more about Angle Bisector Theorem of the Triangle: