Answer :

We have described the theorems which can be used to prove triangles are similar.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion as the two sides of another triangle, and the angle inscribed by the two sides in both triangles are equal, then two triangles are said to be similar.

Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

From the congruency,

AB/XY = BC/YZ = AC/XZ

and ∠B = ∠Y and ∠C = ∠Z

SSS or Side-Side-Side Similarity

If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

From this result, we can conclude that-

∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z

Hence, we have described the theorems which can be used to prove triangles are similar.

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