Question

Similar Figures in the Coordinate Plane Quick Check 4 of 54 of 5 Items Question A dilation creates two similar triangles, ΔMNP∼ΔTUV . To use the SSS (Side-Side-Side) Similarity Theorem, which must be true?(1 point) Responses ∠M≅∠V and ∠N≅∠U angle cap m is congruent to angle cap v and angle cap n is congruent to angle cap u MNTU=MPUV=NPMN cap m cap n over cap t cap u is equal to cap m cap p over cap u cap v is equal to cap n cap p over cap m cap n MNTU=NPUV and ∠N≅∠U cap m cap n over cap t cap u is equal to cap n cap p over cap u cap v and angle cap n is congruent to angle cap u MNTU=MPTV=NPUV cap m cap n over cap t cap u is equal to cap m cap p over cap t cap v is equal to cap n cap p over cap u cap v Skip to navigation page 21 of 21 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To establish that two triangles, ΔMNP and ΔTUV, are similar using the Side-Side-Side (SSS) Similarity Theorem, the ratios of the lengths of corresponding sides must be equal. This means:

If \( MN \), \( NP \), and \( MP \) are the sides of triangle ΔMNP, and \( TU \), \( UV \), and \( TV \) are the sides of triangle ΔTUV, then the following must be true:

\[ \frac{MN}{TU} = \frac{NP}{UV} = \frac{MP}{TV} \]

Therefore, the correct option that states the necessary conditions for using the SSS Similarity Theorem is:

\[ MNTU=\frac{MN}{TU}=\frac{NP}{UV}=\frac{MP}{TV} \]

This reflects the requirement that the ratios of corresponding sides are equal. The angles (like ∠M≅∠V and ∠N≅∠U) do not need to be referenced for the SSS similarity since this theorem strictly focuses on the side lengths.