Triangle DEF is rotated 270° clockwise about the origin. The image of this transformation is triangle LMN, as shown in the figure.Which statement is true?Segment EF is congruent…

Question

asked Sep 22, 2023 178k views

1 Answer

Kevinpeterson · Answer 1 · 2023-09-26T04:47:57+0000

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define Rotation

Rotation does not affect the measures of the corresponding sides of a triangle and its image. Neither does it affect the measures of the angles.

STEP 2: Write the corresponding sides

$\begin{gathered} \triangle DEF\text{ and }\triangle LMN \\ DE\cong LM \\ EF\cong MN \\ DF\cong LN \end{gathered}$

STEP 3: Write the measures of the angles

$\begin{gathered} \begin{equation*} \triangle DEF\text{ and }\triangle LMN \end{equation*} \\ D\cong L \\ E\cong M \\ F\cong N \end{gathered}$

From the explanation in Step 2, therefore, the true statement from the options is "Segment DE is congruent to segment LM"