In the figure below, △DGH was dilated and then rotated 180∘ about point G to create the other triangle. Based on the given transformations, which statement must be true? ∠D=∼∠K and ∠H=∼∠F, so △DGH−△KGF ∠D=∼∠F and ∠H=∼∠K, so △DGH−△FGK ∠D=∼∠K and ∠H=∼∠F, so △DGH=∼△KGF ∠D=∼∠F and ∠H=∼∠K, so △DGH=∼△FGK

Question

In the figure below, △DGH was dilated and then rotated 180∘ about point G to create the other triangle.    Based on the given transformations, which statement must be true?  ∠D=∼∠K and ∠H=∼∠F, so △DGH−△KGF  ∠D=∼∠F and ∠H=∼∠K, so △DGH−△FGK  ∠D=∼∠K and ∠H=∼∠F, so △DGH=∼△KGF  ∠D=∼∠F and ∠H=∼∠K, so △DGH=∼△FGK

Laith Petty · Accepted Answer

Step 1  Given information:  There are two triangles △DGH and △KGF where △DGH is dilated and rotated 180∘ from point G.  Explanation:  If the △DGH is rotated 180∘ from point G then ∠D=∼∠F and ∠H=∼∠K.  Here △DGH is dilated. Therefore, both the triangles cannot be congruent since the shapes are equal but not size.  Step 2  Therefore, both the triangles are similar, by AA similarity.  Answer: Thus, second option is correct.  ∠D=∼∠F and ∠H=∼∠K, so △DGH∼△FGK

In the figure below, \triangle DGH was dilated and then rotated 180^{\circ} about point G to create the other triangle.

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