a) In the given triangles : ABC & FLE
The ratio of coorespodings sides are :
[tex]\frac{AB}{FL}=\frac{6}{6},\text{ }\frac{BC}{LE}=\frac{4.5}{4.5},\text{ }\frac{CA}{EF}=\frac{7.5}{7.5}[/tex]as the ratio of the corresponiding sides are equal to 1
If the ratio of corresponding sides of two triangles are equal then the triangles are similar
Thus, Triangle ABC is similar to triangle FLE
[tex]\Delta ABC\approx\Delta FLE[/tex]b) In the given two triangles : ABC & FLE
The length of corresponding sides of triangle are equal
AB = FL = 6
BC = LE = 4.5
CA = EF = 7.5
All the sides are equal, thus by Side Side Side Congurency, triangle ABC and FLE are congurent
[tex]\Delta ABC\cong\Delta FLE[/tex]c)
[tex]\begin{gathered} \text{ Similar symbol is : }\approx \\ \text{Congureny sysmbol is :}\cong \end{gathered}[/tex]In similar triangles, the side ratio should be equal where as in congurent the sides should be equal.
As if all the sides are equal then, the corresponding sides ratio are equal to 1, thus they varify the property of similar triangle,
Hence, Triangle are also similar if all sides are equal
It concluded that : All congurent triangles are similar triangle but all similar triangle are not congurent.
The mathematics choose the symbol ≅, because it show a sign of equal and by ~ it show similar.
