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 = 1/2 pp all line segments that connect a point on the pre - image to its corresponding point on the image are parallel

Explanation:

Step1: Properties of translation

In a translation, every point of the pre - image is moved the same distance in the same direction. So, the lengths of the segments connecting corresponding points (e.g., \( LL'\), \( MM'\), \( NN'\), \( PP'\)) are equal. That is \( LL'=MM' = NN'=PP'\). So \( LL' = PP'\) and \( LL' = MM'\) are True.

Step2: Congruence in translation

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

Step3: Parallelism in translation

Since each point is moved the same distance in the same direction, all line segments that connect a point on the pre - image to its corresponding point on the image are parallel.

The statement \( NN'=\frac{1}{2}PP'\) is False because \( NN' = PP'\) (due to the property of translation where all translation vectors for corresponding points are equal).

Answer:

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