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The graph shows triangle A B C is congruent to triangle D E F ​by S A S, where segment C A is congruent to segment F D, segment C B is congruent to segment F E, and angle C is congruent to angle F

Move the statements to the table to create a series of transformations that will map triangle A B C onto triangle D E F to show that the two triangles are congruent.
What is Transformation 1 and. Transformation 2

The graph shows triangle A B C is congruent to triangle D E F ​by S A S, where segment-example-1
User Yejin
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2 Answers

6 votes

reflection on x-axis

then translations right 3 units & down 2 units

User Tomas Reimers
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8.0k points
10 votes

To map triangle ABC onto triangle DEF by SAS congruence, Transformation 1 involves a translation where points A, B, and C move to D, E, and F respectively. Transformation 2 is a 180-degree rotation around point F.

To create a series of transformations mapping triangle ABC onto triangle DEF:

1. Transformation 1 - Translation:

- Translation is the first transformation. It involves moving the entire triangle in a specific direction.

-
\(A(-2, 4) \rightarrow D(1, -2)\)

-
\(B(-1, 3) \rightarrow E(2, -1)\)

-
\(C(-3, 2) \rightarrow F(0, 0)\)

2. Transformation 2 - Rotation:

- After translation, a rotation is performed around a specific point.

- In this case, it's a 180-degree rotation, as angle C is congruent to angle F.

-
\(D(1, -2) \rightarrow D'(1, 2)\)

-
\(E(2, -1) \rightarrow E'(-2, 1)\)

-
\(F(0, 0) \rightarrow F'(0, 0)\)

So, Transformation 1 is a translation, and Transformation 2 is a rotation of 180 degrees.

User Bhanuka Manesha
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8.3k points

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