Question

WILL MARK BRAINLYIEST!!!! Ellie drew ΔLMN, in which m∠LMN = 90°. She then drew ΔPQR, which was a dilation of ΔLMN by a scale factor of one half from the center of dilation at point M. Which of these can be used to prove ΔLMN ~ ΔPQR by the AA similarity postulate?

Answer 1

Answer:

Please refer to the image attached to this answer.

Step-by-step explanation:

we have ΔLMN as our parent triangle, where M=90°. Another triangle ΔPQR is formed which was dilation of ΔLMN with a factor of one and half that is 1.5

We are also given that the center of dilation is M itself . Hence the point Q of the ΔPQR overlap with the M.  

Now let us see the image attached with this. The Line LM and MN are extended further till Point P and R respectively.  

If LN = x and MN = y  

PM = 1.5x and MR = 1.5y  

as the scale of dilation is 1.5

Now let us see the the ratio of the sides of the two triangles.

$\frac{LM}{MN}=\frac{x}{y}$

$\frac{PM}{MR}=\frac{1.5 \times x}{1.5 \times y}$

$=\frac{x}{y}$

Hence the ratio of the sides is same. There for the triangles are similar to each other.