To answer this question, we can see that:
Then, we have that both triangles are similar triangles since the side CB and XY are parallel and then the interior angles are congruent. Then, we can write the next proportions:
[tex]\frac{CB}{XY}=\frac{AC}{AX}=\frac{AB}{AY}[/tex]
We have that the ratio between CB and XY is:
[tex]\frac{CB}{XY}=\frac{8}{4}\Rightarrow\frac{CB}{XY}=2[/tex]
In other words, we can say that the side CB is twice the measure of side XY or:
[tex]\frac{CB}{XY}=\frac{AC}{AX}=\frac{AB}{AY}=2[/tex]
And we can also say that:
[tex]\frac{XY}{CB}=\frac{AX}{AC}=\frac{AY}{AB}=\frac{1}{2}[/tex]
Using these proportions is easy to find the values of AX and AY as follows:
Finding the value of AX
We have that AC = 14cm, then:
[tex]\frac{AX}{AC}=\frac{1}{2}\Rightarrow AX=\frac{1}{2}\cdot AC\Rightarrow AX=\frac{1}{2}\cdot14\operatorname{cm}\Rightarrow AX=7\operatorname{cm}[/tex]
Finding the value of AY
We have that AB = 18cm, then we have:
[tex]\frac{AY}{AB}=\frac{1}{2}\Rightarrow AY=\frac{1}{2}\cdot AB\Rightarrow AY=\frac{1}{2}\cdot18\operatorname{cm}\Rightarrow AY=9\operatorname{cm}[/tex]
In summary, therefore, the value for AX = 7cm, and the value for AY = 9cm.
