AA Criterion for Similar Triangles, Part 2As you saw in the previous activity, knowing that one pair of corresponding angle measures in two triangles is equal is not enough to prove that they are similar. Some additional information must be required to prove triangle similarity. Next you’ll investigate whether two pairs of corresponding angles in two triangles having equal angle measures is necessary and sufficient to prove that the triangles are similar. Open GeoGebra again, and complete each step below.Part ACreate a random triangle, ∆ABC. Measure and record its angles.Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment, , parallel to the line segment you located on ∆ABC. You can draw of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC.From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC.Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.Take a screenshot of your results, save it, and insert the image in the space below.Record all three angle measurements of ∆DEF in the table below. Angle∠DEF∠EFD∠FDE measurementsPart DHow do the angles of ∆DEF compare with those in the original triangle? In particular, compare the angle that you did not set in ∆DEF with the Part EWith two of the angles fixed on ∆DEF, what do you notice about the shape of ∆DEF when compared with ∆ABC?Pick any side of ∆DEF, and find its length. Find the ratio (n) of this side to the corresponding side of ∆ABC.Dilate ∆ABC about the origin using the scale factor n. Measure and compare the lengths of the sides of the dilated triangle, ∆A'B'C', with those of ∆DEF. Take a screenshot of your dilation, save it, and insert the image below the table.What can you conclude about ∆A'B'C' and ∆DEF based on their side lengths, angle measures, or both?Explain why there must be a sequence of rigid transformations that will map ∆A'B'C' exactly onto ∆DEF. Find and perform one such sequence of rigid transformations. Describe the sequence of rigid transformations you performed.Part JBased on your responses to parts H and I, what can you conclude about ∆ABC and ∆DEF? Explain your answer in terms of similarity transformations.Part KTo decide whether two triangles are similar, is it enough to know that two pairs of corresponding angle measures in the triangles are equal? Use your observations and your understanding of similarity to explain your answer.