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Triangles DEF and GHI are shown. Which sequence of rotations, reflections, and/or translations would map triangle DEF onto triangle GHI?

Does mapping triangle DEF onto triangle GHI prove the two triangles are congruent? Explain your reasoning.

Answer:

Part A:

The sequence of transformation that maps triangle DEF to triangle GHI are;

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Part B:

1) Yes

2) The points of the triangle GHI obtained from the mapping of triangle DEF using the given transformation are corresponding therefore, the mapping proves that the two triangles are congruent

Step-by-step explanation:

Part A:

The given coordinates of the vertices of triangle DEF are;

F(-1, 5), D(-5, 2), and E(-3, 1)

The given coordinates of the vertices of triangle IHG are;

I(1, -1), H(3, -5), and G(5, -4)

Therefore, the transformation that maps ΔDEF to ΔGHI are

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Reflection of point F(-1, 5) across the y-axis gives → (1, 5)

Followed by a translation 6 units down gives;

(1, 5) →T(y - 6) → I(1, -1)

Reflection of point D(-5, 2) across the y-axis gives → (5, 2)

Followed by a translation 6 units down gives;

(5, 2) →T(y - 6) → G(5, -4)

Reflection of point E(-3, 1) across the y-axis gives → (3, 1)

Followed by a translation 6 units down gives;

(3, 1) →T(y - 6) → H(3, -5)

Part B:

1) Yes mapping triangle DEF onto triangle GHI proves that the two triangles are congruent

2) The points of the triangle GHI obtained from the mapping of triangle DEF are the same, therefore, the mapping proves that the two triangles are congruent

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