Asked by john
01:52:27
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
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Answer: "because ∠MNL and ∠ONP are congruent angles."
Reason: If the angle at N in triangle LMN equals the angle at N in triangle PON, you can rotate triangle LMN about N to make its two rays coincide with the two rays of triangle PON, and then dilate about N to scale the side lengths to match. A rotation about N plus a dilation about N is a similarity (a spiral similarity) that sends one triangle to the other, so the triangles are similar.
Reason: If the angle at N in triangle LMN equals the angle at N in triangle PON, you can rotate triangle LMN about N to make its two rays coincide with the two rays of triangle PON, and then dilate about N to scale the side lengths to match. A rotation about N plus a dilation about N is a similarity (a spiral similarity) that sends one triangle to the other, so the triangles are similar.
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