Question

If a series of rigid transformations maps ∠f onto ∠c where ∠f is congruent to ∠c, then which of the following statements is true?

1) Triangles ABC and FDE, in which angles A and D are right angles ΔABC ≅ ΔDEF because of the definition of similarity in terms of similarity transformations
2) Triangles ABC and EDF, in which angles A and D are right angles ΔABC ≅ ΔEDF because of the AA similarity postulate
3) Segment AC ≅ Segment DF because corresponding parts of similar triangles are proportional
4) Segment BC ≅ Segment DE because of the definition of similarity in terms of similarity transformations

Answer 1

In a series of rigid transformations, if angle ∠f is congruent to angle ∠c, then the corresponding sides and angles of the triangles will be congruent. The AA (Angle-Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Therefore, if ∠f is congruent to ∠c, and other conditions are met (such as right angles at A and D), then triangles ABC and EDF are similar by the AA similarity postulate.

The correct statement is: 2) Triangles ABC and EDF, in which angles A and D are right angles ΔABC ≅ ΔEDF because of the AA similarity postulate

In a series of rigid transformations, if angle ∠f is congruent to angle ∠c, then the corresponding sides and angles of the triangles will be congruent.

The AA (Angle-Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Therefore, if ∠f is congruent to ∠c, and other conditions are met (such as right angles at A and D), then triangles ABC and EDF are similar by the AA similarity postulate.

Answer 2

The correct statement is option 2) Triangles ABC and EDF, in which angles A and D are right angles ΔABC ≅ ΔEDF because of the AA similarity postulate.

Step-by-step explanation:

The correct statement is 2) Triangles ABC and EDF, in which angles A and D are right angles ΔABC ≅ ΔEDF because of the AA similarity postulate.

To prove that two triangles are congruent, we need to show that they have congruent corresponding parts. In the given scenario, the congruence of angles A and D (both being right angles) establishes that triangles ABC and EDF are similar. And since ∠f is congruent to ∠c, it means that the angles in triangles ABC and EDF correspond to each other. Therefore, option 2) is true.