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

1.) Translate triangle ABC so that point C lies on point D to confirm ∠C ≅ ∠D.
2.) Dilate ΔABC from point A by the ratio segment AD over segment AB to confirm segment AD ~ segment AB.
3.) Translate triangle ABC so that point B lies on point D to confirm ∠B ≅ ∠D.
4.) Dilate ΔABC from point A by the ratio segment AE over segment AC to confirm segment AE ~ segment AC.

Answer 1

The correct transformation to prove triangle similarity by the AA postulate is dilating ΔABC from point A by the ratio of segment AE to AC. Therefore correct option is 4

Step-by-step explanation:

If angle A is congruent to itself by the Reflexive Property, the transformation that could be used to prove ΔABC ~ ΔADE by AA similarity postulate is dilating ΔABC from point A by the ratio of segment AE over segment AC to confirm segment AE ~ segment AC. This means that we are looking at corresponding angles and sides and comparing their ratios to find if the triangles are similar by Angle-Angle (AA) similarity.

Option 4 suggests this method: Dilate ΔABC from point A by the ratio segment AE over segment AC to confirm segment AE ~ segment AC. By dilating the triangle in such a way, we ensure that the sides are proportional while maintaining the congruency of angle A, which would meet the requirements for proving similarity by AA (Angle-Angle).