Question

If angle a is congruent to itself by the reflexive property, which transformation could be used to prove δabc ~ δade by aa similarity postulate? triangles abc and ade, in which point b is between points a and d and point c is between points a and e translate triangle abc so that point c lies on point d to confirm ∠c ≅ ∠d. dilate δabc from point a by the ratio segment ad over segment ab to confirm segment ad ~ segment ab. translate triangle abc so that point b lies on point d to confirm ∠b ≅ ∠d. dilate δabc from point a by the ratio segment ae over segment ac to confirm segment ae ~ segment ac.

Answer 1

To prove ΔABC and ΔADE similar by AA, we can dilate ΔABC from point A with a ratio of AD:AB to confirm the second pair of congruent angles.

Step-by-step explanation:

To prove that triangles ΔABC and ΔADE are similar by the AA (Angle-Angle) Similarity Postulate, we need to show that two angles in one triangle are congruent to two angles in the other triangle. Since angle a is congruent to itself by the reflexive property, we need to establish the congruence of one more pair of angles.

The correct transformation to use would be to dilate ΔABC from point A by the ratio of segment AD over segment AB. This dilation would scale the triangle in such a way that ΔADE would be a scaled version of ΔABC, confirming the second set of angles are congruent — thus establishing AA similarity.