Question

Reflect δECD over segment AC. This establishes that ________. Then, translate point E′ to point A. This establishes that ________. Therefore, δACB ~ δECD by the AA similarity postulate.

a) ∠ABC ≅ ∠E′D′C′;
b) ∠E′D′C′ ≅ ∠ABC
c) ∠ACB ≅ ∠E′C′D′; ∠D′E′C′ ≅ ∠BAC
d) ∠ACB ≅ ∠E′C′D′; ∠E′D′C′ ≅ ∠ABC

Answer 1

Reflecting triangle ∆ECD over line segment AC and translating point E' to A shows that triangles ∆ACB and ∆E' C' D' are similar by the AA similarity postulate, confirming that their corresponding angles are congruent.

Step-by-step explanation:

The question deals with the principles of geometry, specifically the reflection of a triangle over a line and subsequent translations of one of its points.

Reflecting triangle ∆ECD over segment AC means that every point of ∆ECD will be mirrored across the line segment AC, creating a congruent triangle ∆E' C' D'. Reflecting over AC will produce congruent corresponding angles, therefore, ∆ABC ≃ ∆E' D' C'.

Then, when we translate point E' to point A, it indicates that we are moving point E' to point A without altering the shape or orientation of the triangle. This translation would prove that ∆ACB ≃ ∆E' C' D' by the AA (Angle-Angle) similarity postulate, suggesting that the two angles at each vertex are congruent, establishing similarity between the triangles.