Question

Shaun drew ΔLMN, in which m∠LMN = 90°. He then drew ΔPQR, which was a dilation of ΔLMN by a scale factor of 3 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:

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.

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