Given:
In triangle DEF, HG is parallel to DF.
To find:
The value of x.
Solution:
In triangles DEF and GEH,
[tex]\angle DE F\cong \angle GEH[/tex] (Common angle)
[tex]\angle EDF\cong \angle EGH[/tex] (Corresponding angle)
[tex]\Delta DE F\sim \Delta GEH[/tex] (By AA property of similarity)
We know that corresponding sides of similar triangle are proportional.
[tex]\dfrac{DE}{GE}=\dfrac{DF}{GH}[/tex]
[tex]\dfrac{9+(x+5)}{x+5}=\dfrac{12}{6}[/tex]
[tex]\dfrac{x+14}{x+5}=2[/tex]
[tex]x+14=2(x+5)[/tex]
[tex]x+14=2x+10[/tex]
Isolating variable terms, we get
[tex]x-2x=-14+10[/tex]
[tex]-x=-4[/tex]
[tex]x=4[/tex]
Therefore, the value of x is equal to 4.
