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SSS similarity theorem states: If the corresponding sides of two triangles are proportional, then the two triangles are similar.

You have two isosceles triangle, then if

[tex]\dfrac{44}{20}=\dfrac{x}{35},\\ \\x=\dfrac{44\cdot 35}{20}=11\cdot 7=77,[/tex]

two isosceles triangles will be similar by SSS theorem.

Answer: correct choice is C.

The value of x that will make the triangles similar by SSS similarity theorem is;

x = 77.

We are told that the 2 triangles are similar by SSS theorem.

Now, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Thus, in our 2 given triangles ,applying the SSS postulate gives;

x/35 = 44/20

Applying the multiplication property of equality, let us multiply both sides by 35 to get;

x = (44 * 35)/20

x = 77

Thus, in conclusion the value of x that will make the triangles similar by SSS similarity theorem is 77.

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