Question

reflect the figure across the y - axis. then decide if each statement about reflected figures is true or false.
your answer
statement about reflected figures true false
if two sides are parallel in the original figure, then those sides are parallel in the final figure.
the final angle measures are the same as the original angle measures.
the final side lengths are longer than the original side lengths.
the original figure and the final figure are congruent.

Explanation:

Step1: Properties of Reflection

Reflection is a rigid transformation. Rigid transformations preserve the shape and size of the figure. Parallelism of lines is also preserved under reflection.

Step2: Analyzing Each Statement

• First Statement:

Since reflection is a rigid transformation and parallelism is preserved. If two sides are parallel in the original figure, they are parallel in the reflected figure. So, the statement "If two sides are parallel in the original figure, then those sides are parallel in the final figure" is True.

• Second Statement:

Reflection does not change the angle measures of a figure. So, the statement "The final angle measures are the same as the original angle measures" is True.

• Third Statement:

Reflection is a rigid transformation which means side - lengths are preserved. So, the statement "The final side lengths are longer than the original side lengths" is False.

• Fourth Statement:

Since reflection preserves side - lengths and angle measures (rigid transformation), the original and reflected figures are congruent. So, the statement "The original figure and the final figure are congruent" is True.

Answer:

1. True
2. True
3. False
4. True