Questions: Percy wants to use rigid transformations to show that triangle GHI is congruent to triangle LKJ as a way of confirming the SSS triangle congruence criterion. She starts by translating triangle GHI along a vector that Option #1: Percy did not make a mistake. The fact that the triangles do not overlap means that the triangles must not be congruent. Option #2: Percy made a mistake and did not reflect over the correct line segment. She should have reflected triangle G'H'I' across vector GH when creating triangle G"H"I". Option #3: Percy made a mistake and did not match corresponding points correctly. She should have translated triangle GHI along a vector that takes point G to point L when creating triangle G'H'I'.

Percy wants to use rigid transformations to show that triangle GHI is congruent to triangle LKJ as a way of confirming the SSS triangle congruence criterion. She starts by translating triangle GHI along a vector that

Option #1: Percy did not make a mistake. The fact that the triangles do not overlap means that the triangles must not be congruent.

Option #2: Percy made a mistake and did not reflect over the correct line segment. She should have reflected triangle G'H'I' across vector GH when creating triangle G"H"I".

Option #3: Percy made a mistake and did not match corresponding points correctly. She should have translated triangle GHI along a vector that takes point G to point L when creating triangle G'H'I'.

Transcript text: Percy wants to use rigid transformations to show that $\triangle G H I \cong \triangle L K J$ as a way of confirming the SSS triangle congruence criterion. She starts by translating $\triangle G H I$ along a vector that Option \#1: Percy did not make a mistake. The fact that the triangles do not overlap means that the triangles must not be congruent. Option \#2: Percy made a mistake and did not reflect over the correct line segment. She should have reflected $\triangle G^{\prime} H^{\prime} I^{\prime}$ across $\overrightarrow{G^{\prime} H}$ when creating $\triangle G " H$ " $I$ ". Option \#3: Percy made a mistake and did not match corresponding points correctly. She should have translated $\triangle G H I$ along a vector that takes point $G$ to point $L$ when creating $\triangle G^{\prime} H^{\prime} I^{\prime}$.

Solution

Solution Steps

Step 1: Understand the Problem

Percy wants to use rigid transformations to show that ΔGHI ≅ ΔLKJ using the SSS triangle congruence criterion. She starts by translating ΔGHI along a vector that takes point G to point J to create ΔG'H'I' (2). She then reflects ΔG'H'I' across G'H' to create ΔG''H''I'' (3). She notices that the triangles do not appear to overlap.

Step 2: Analyze the Options

Option #1: Percy did not make a mistake. The fact that the triangles do not overlap means that the triangles must not be congruent.
Option #2: Percy made a mistake and did not reflect over the correct line segment. She should have reflected ΔG'H'I' across G'H' when creating ΔG''H''I''.
Option #3: Percy made a mistake and did not match corresponding points correctly. She should have translated ΔGHI along a vector that takes point G to point L when creating ΔG'H'I'.

Step 3: Evaluate the Transformations

Translation: Percy translated ΔGHI along a vector that takes point G to point J. This should create ΔG'H'I' with G' at J, H' at a point corresponding to H, and I' at a point corresponding to I.
Reflection: Percy then reflected ΔG'H'I' across G'H'. If done correctly, this should create ΔG''H''I'' with G'' at a point corresponding to G', H'' at a point corresponding to H', and I'' at a point corresponding to I'.

Step 4: Identify the Mistake

Reflection Line: The reflection should be across the line segment G'H', but the resulting ΔG''H''I'' does not overlap with ΔLKJ, indicating a mistake in the reflection process.

Final Answer

Option #2 best describes what happened. Percy made a mistake and did not reflect over the correct line segment. She should have reflected ΔG'H'I' across G'H' when creating ΔG''H''I''.

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