To prove ΔONP and ΔMNL similar by the AA similarity postulate, we can use the following method and additional information:
1. Use a rigid transformation to prove that ∠NPO ≅ ∠NLM:
- Since line k intersects both triangles at point N, we can show that ∠NPO ≅ ∠NLM by a rotation or reflection that preserves the angles.
2. Use rigid and nonrigid transformations to prove segment PN over segment MN = segment LN over segment ON:
- By showing that segment PN over segment MN = segment LN over segment ON through a combination of translations and dilations that maintain the proportions of the sides.
3. Use rigid and nonrigid transformations to prove segment PN over segment ML = segment LN over segment ON:
- Similar to the previous step, we can use a combination of translations and dilations to demonstrate that segment PN over segment ML = segment LN over segment ON.
4. Use a rigid transformation to prove that ∠NLM ≅ ∠LMN:
- By applying a rotation or reflection that preserves the angles, we can show that ∠NLM ≅ ∠LMN.
By utilizing these transformations and the given information, we can establish the similarity between ΔONP and ΔMNL using the AA similarity postulate.
Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?
Segments OM and LP intersect at point N; triangles are formed by points LNM and ONP; line k intersects with both triangles at point N.
Use rigid and nonrigid transformations to prove segment PN over segment MN = segment LN over segment ON.
Use a rigid transformation to prove that ∠NPO ≅ ∠NLM.
Use rigid and nonrigid transformations to prove segment PN over segment ML = segment LN over segment ON.
Use a rigid transformation to prove that ∠NLM ≅ ∠LMN.
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