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Plot point F so that TriangleABC is congruent with TriangleFGH. Identify a sequence of rigid motions that maps TriangleABC onto TriangleFGh and use a theorem to complete the explanation of why the triangles are congruent

Plot Point F So That TriangleABC Is Congruent With TriangleFGH Identify A Sequence Of Rigid Motions That Maps TriangleABC Onto TriangleFGh And Use A Theorem To class=

Sagot :

Okay, let's break this down step-by-step:

1. To make Triangle ABC congruent to Triangle FGH, we need to translate point F so that side lengths AB, BC, and CA map to FG, GH, and HF respectively.

2. From the given side length formulas, we can see that:

  AB = BC = CA = sqrt(2)

  FG = sqrt(5)

  GH = sqrt(2)

3. To map AB to FG, and BC to GH, point F should be plotted at (1,2). This will make FG = sqrt(5) and GH = sqrt(2), matching AB and BC respectively.

4. With point F at (1,2), HF will also equal sqrt(2), matching CA. So Triangle ABC will be congruent to Triangle FGH.

5. The sequence of rigid motions:

  - Translate Triangle ABC so that point A maps to point F (1,2)

  - Reflect the translated triangle over line FG

6. By the SSS (Side-Side-Side) Congruence Theorem, Triangle ABC is congruent to Triangle FGH, since all corresponding sides (AB & FG, BC & GH, CA & HF) are equal.

Therefore, plotting point F at (1,2) and applying the translation and reflection described will map Triangle ABC onto Triangle FGH, making the triangles congruent by the SSS theorem.

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