The correct answer is option B which is the length of the segment Ab will be [tex]AB = AX \dfrac{AY}{AC}[/tex].
What is congruency?
The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.
As we can see in the question the two triangles AXY and ABC are similar to each other so the ratio of the sides AB and AX will be equal to the ratio of the sides AY and AC.
The ratio will be given as:-
[tex]\dfrac{AB}{AX}=\dfrac{AY}{AC}[/tex]
[tex]AB =AX\dfrac{AY}{AC}[/tex]
Therefore the correct answer is option B which is the length of the segment Ab will be [tex]AB = AX \dfrac{AY}{AC}[/tex].
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