Question

Type the correct answer in each box. Spell all the words correctly, and use numerals instead of words for numbers. If necessary, use / for the tion bar(s). We can show that AABC is congruent to AA BC by a translation of ____ units and a ____ across the ____ -axis.

a) 2, reflection, y-axis
b) 3, rotation, x-axis
c) 4, translation, y-axis
d) 5, dilation, x-axis

Answer 1

The provided exercise is a high school level Math problem seeking the right combination of geometric transformations to prove two triangles congruent.

Step-by-step explanation:

The question pertaining to congruent triangles under geometric transformations such as translations and reflections across the y-axis or x-axis falls under the topic of Geometry, which is a branch of Mathematics. In this specific scenario, the student is asked to determine how triangle AABC can be shown to be congruent to triangle A' B' C' through one of the given geometric transformations. Option (a), which suggests a translation of 2 units and a reflection across the y-axis, seems appropriate if it leads to the superimposition of triangle AABC onto triangle A' B' C'. The key task is to discern the correct transformation that will position one triangle onto the other, maintaining congruency, which means all corresponding sides and angles are equal. This kind of problem requires a solid understanding of congruence transformations in a coordinate plane.