The SSS Congruence Theorem Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items

Question
Use the image to answer the question.

Three separate images, are side by side. In images 2 and 3 the triangles overlap by movement along a vector, and a flip along the hypotenuse.

Percy wants to use rigid transformations to show that △GHI≅△LKJ
as a way of confirming the SSS triangle congruence criterion (1). She starts by translating △GHI
along a vector that takes point G
to point J
to create △G′H′I′
(2). She then reflects △G′H′I′
across G′I¯¯¯¯¯¯¯¯′
to create △G"H"I"
(3). She notices that the triangles do not appear to overlap. What happened?

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 △G′H′I′
across G′H¯¯¯¯¯¯¯¯¯¯′
when creating △G"H"I"
.

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

(1 point)
Option #
best describes what happened.

Answer 1

Based on the information provided, the best option that describes what happened is:

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 \( \triangle G'H'I' \).

This option makes sense because for the two triangles to be congruent, they need to be properly aligned in corresponding positions. Translating from \( G \) to \( J \) rather than \( L \) would prevent the triangles from overlapping, indicating that they have not been positioned correctly.