Asked by Toxic
Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.
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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Answer: because ∠MNL and ∠ONP are congruent angles.
Explanation: the congruent angles at the common vertex N mean the angle between the two rays of triangle LMN (NM and NL) equals the angle between the two rays of triangle PON (NO and NP). A rotation about N can carry the rays NM and NL to NO and NP, and a dilation about N can scale the distances along those rays so the corresponding vertices coincide. That composition (rotation then dilation) carries △LMN to △PON, so the triangles are similar.
Explanation: the congruent angles at the common vertex N mean the angle between the two rays of triangle LMN (NM and NL) equals the angle between the two rays of triangle PON (NO and NP). A rotation about N can carry the rays NM and NL to NO and NP, and a dilation about N can scale the distances along those rays so the corresponding vertices coincide. That composition (rotation then dilation) carries △LMN to △PON, so the triangles are similar.
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