Question

1. triangle xyz has been enlarged with p as the center of dilation to form triangle xyz. which two conclusions are correct? select the best answers. $\frac{xy}{xy}=\frac{yz}{yz}=\frac{xz}{xz}$ $delta xyzcongdelta xyz$ $\frac{yz}{yz}=\frac{xz}{xz}=\frac{xy}{xz}$ $xx = yy = zz$ $delta xyzsimdelta xyz$

Explanation:

Step1: Recall dilation property

Dilation creates similar figures. For two similar triangles $\triangle XYZ$ and $\triangle X'Y'Z'$ formed by dilation, the ratios of corresponding - side lengths are equal. That is, $\frac{XY}{X'Y'}=\frac{YZ}{Y'Z'}=\frac{XZ}{X'Z'}$.

Step2: Understand similarity notation

The symbol $\sim$ is used for similarity. When a triangle is dilated, the original triangle and the dilated triangle are similar, i.e., $\triangle X'Y'Z'\sim\triangle XYZ$. The symbol $\cong$ is for congruence, and dilation changes the size (except when the scale - factor is 1), so the triangles are not congruent. Also, $X'X$, $Y'Y$, and $Z'Z$ are not equal in general as they depend on the position of the center of dilation and the vertices.

Answer:

$\frac{XY}{X'Y'}=\frac{YZ}{Y'Z'}=\frac{XZ}{X'Z'}$, $\triangle X'Y'Z'\sim\triangle XYZ$