asapgraph the image of the given triangle after the transformation that has the rule (x, y)→(x+3, y−2) . this is the triangle before you transform it.

From the figure, the vertices of the given triangle are
(-3,4), (1,3) and (5,5).

The given transformation is (x,y) -> (x+3, y-2).
Therefore the coordinates of the transformed triangle are
(-3+3,4-2), (1+3,3-2), (5+3,5-2) = (0,2), (4,1), (8,3)

The transformed triangle is shown in red color.

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If two sides of a triangle are congruent, then the angles opposite those sides are congruent. the converse of the base angles theorem, states that if two angles of a triangle are congruent, then sides opposite those angles are congruent.