Question

If ΔONP is dilated from point N by a scale factor of segment NL over segment NP, which additional transformation could determine if ΔONP and ΔMNL are 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.

Rotate O'N'P' 180° about point N.
Rotate O'N'P' 90° clockwise about point N.
Translate point P' to point M.
Translate point O' to point L.

Answer 1

The answer is to rotate O"N"P 180 Degrees by point N

Explanation:

This will show the similarity between the two triangles angles.

Answer 2

Rotate O'N'P' 180° about point N.

Explanation:

From the description of the figure:

∠ONP ≅ ∠LNP (opposite angles)

∠MOP ≅ ∠LMO (alternate angles)

∠LPO ≅ ∠PLM (alternate angles)

If ΔONP is dilated from point N by a scale factor of segment NL over segment NP, then a triangle ΔO'N'P' is formed which all sides proportional to sides of ΔONP.

After a rotation of ΔO'N'P' 180° about point N, the triangle ΔMNL is formed. AA similarity postulate is satisfied because angles are congruent and sides are proportional.