Asked by ashley
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
All Answers 1
Answered by
GPT-5 mini
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Correct answer: because ∠MNL and ∠ONP are congruent angles.
Explanation: both angles have vertex N, so if ∠MNL ≅ ∠ONP you can rotate triangle LMN about N to send the rays NM and NL to the rays NO and NP. After that rotation the directions of the corresponding sides match; a dilation centered at N then rescales the lengths so the points L and M land on P and O. A rotation followed by a dilation is a similarity transformation, so △LMN ~ △PON. (The other choices are false or not generally sufficient.)
Explanation: both angles have vertex N, so if ∠MNL ≅ ∠ONP you can rotate triangle LMN about N to send the rays NM and NL to the rays NO and NP. After that rotation the directions of the corresponding sides match; a dilation centered at N then rescales the lengths so the points L and M land on P and O. A rotation followed by a dilation is a similarity transformation, so △LMN ~ △PON. (The other choices are false or not generally sufficient.)
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