why is the information in the diagram enough to determine that △lmn ~ △pon using a rotation about point n…
why is the information in the diagram enough to determine that △lmn ~ △pon using a rotation about point n and a dilation? because both triangles appear to be equilateral because ∠mnl and ∠onp are congruent angles because one pair of congruent corresponding angles is sufficient to determine similar triangles because both triangles appear to be isosceles, ∠mln ≅ ∠lmn, and ∠nop ≅ ∠opn
Answer
Explanation:
Step1: Recall similarity - triangle criteria
Two triangles are similar if two pairs of corresponding angles are congruent. In the given triangles $\triangle LMN$ and $\triangle PON$, $\angle MNL$ and $\angle ONP$ are vertical - angles.
Step2: Use vertical - angle property
Vertical angles are always congruent. So, $\angle MNL\cong\angle ONP$. If we can show another pair of congruent angles (which can be achieved by rotation and dilation), we can prove the similarity. The presence of this one pair of congruent angles is a start in the process of showing similarity.
Answer:
because $\angle MNL$ and $\angle ONP$ are congruent angles