Question

if △lmn is dilated by a scale factor of 0.5, which of the following statements is not true? a. the sides of △lmn are congruent to the sides of △lmn. b. the angles of △lmn are congruent to the angles of △lmn. c. △lmn is similar to △lmn. d. △lmn is smaller than △lmn.

Explanation:

Step1: Recall dilation properties

Dilation is a transformation that changes the size of a figure. When a triangle $\triangle LMN$ is dilated by a scale - factor $k = 0.5$, the angles of the pre - image and the image are congruent because dilation is a similarity transformation. That is, $\angle L=\angle L'$, $\angle M=\angle M'$, $\angle N=\angle N'$, so $\triangle LMN\sim\triangle L'M'N'$.

Step2: Analyze side - length relationship

The sides of the image $\triangle L'M'N'$ are related to the sides of the pre - image $\triangle LMN$ by the scale factor. If the scale factor $k = 0.5$, then $L'M'=0.5LM$, $M'N'=0.5MN$, $L'N'=0.5LN$. This means that the sides of $\triangle LMN$ are not congruent to the sides of $\triangle L'M'N'$.

Step3: Analyze size relationship

Since the scale factor $k = 0.5<1$, the triangle $\triangle L'M'N'$ is smaller than $\triangle LMN$.

Answer:

A. The sides of $\triangle LMN$ are congruent to the sides of $\triangle L'M'N'$.