Question

trapezoid lmnp was constructed using trapezoid lmnp. for the transformation to be a translation, which - statements must be true? select four options. ll=pp ll=mm trapezoid lmnp is congruent to trapezoid lmnp. nn = 1/2pp all line segments that connect a point on the pre - image to its corresponding point on the image are parallel.

Explanation:

Step1: Recall translation properties

In a translation, corresponding - points of the pre - image and the image are moved the same distance and in the same direction. So, the lengths of the line - segments connecting corresponding points are equal. That is, for any two corresponding points \(A\) and \(A'\) and \(B\) and \(B'\) in a translation, \(AA' = BB'\). So, \(LL'=MM' = NN'=PP'\).

Step2: Consider congruence

A translation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent. Trapezoid \(LMNP\) is congruent to trapezoid \(L'M'N'P'\).

Step3: Analyze parallelism

In a translation, the line - segments that connect a point on the pre - image to its corresponding point on the image are parallel.

Answer:

A. \(LL' = PP'\)
B. \(LL'=MM'\)
C. Trapezoid \(LMNP\) is congruent to trapezoid \(L'M'N'P'\)
E. All line segments that connect a point on the pre - image to its corresponding point on the image are parallel