In the given triangles, as per given conditions ΔRSY≅ Δ TSX by SAS (Side Angle Side) theorem.
What is triangle?
" Triangle is defined as the two dimensional geometrical shape with three vertices , three sides, and three angles enclosed in it."
Theorem used
SAS theorem ( Side angle side)
In given triangles, corresponding sides and included angle of one triangle is equals to corresponding sides and included angle of another triangle , then triangles are said to be congruent.
According to the question,
Given,
In a triangles,
SX ≅ SY ______ [tex]( 1)[/tex]
XR ≅ YT ______[tex]( 2 )[/tex]
Add [tex](1)[/tex] and [tex](2)[/tex] we get,
SX + XR ≅ SY + YT
⇒SR ≅ ST ____[tex](3)[/tex]
In triangle ΔRSY and ΔTSX,
SY ≅ SX ( given)
∠RSY ≅∠TSX ( Common angle)
SR ≅ ST (from [tex](3)[/tex] )
By SAS theorem (side angle side theorem ) stated above we get,
ΔRSY≅ Δ TSX
Hence, ΔRSY≅ Δ TSX by SAS theorem as per the given condition of a triangle.
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