Question

Triangle ABC is reflected across a vertical line and then translated 8 units down to produce triangle EFG.

A. Side AB is 8 units longer than side EF.
B. Angle ABC is congruent to angle EFG.
C. Side BC is the same length as side FG.
D. Triangle EFG is congruent to triangle ABC.

Answer 1

After reflecting Triangle ABC across a vertical line and translating it, triangle EFG would be congruent to triangle ABC, with corresponding angles and sides being equal in measure.

Step-by-step explanation:

When Triangle ABC is reflected across a vertical line, the resulting triangle will have the same size and angles as the original triangle, making corresponding sides and angles congruent. A translation then shifts the triangle without altering its shape or size. Hence:

• Statement A is incorrect because side AB cannot be 8 units longer than side EF; both will be equal in length.
• Statement B is correct as angle ABC would be congruent to angle EFG due to the properties of reflections and translations.
• Statement C is also correct because side BC will have the same length as side FG after the reflection and translation.
• Statement D is correct, as triangle EFG is congruent to triangle ABC because reflections and translations are rigid motions, which do not change the size or shape of figures.