Question

Which of the following completes the proof? triangles abc and edc are formed from segments bd and ac, in which point c is between points b and d and point e is between points a and c. given: segment ac is perpendicular to segment bd prove: Δacb Δecd reflect Δecd over segment ac. this establishes that ________. then, ________. this establishes that ∠e′d′c′ ≅ ∠abc. therefore, Δacb Δecd by the aa similarity postulate. ∠abc ≅ ∠e′d′c′; translate point e′ to point a ∠acb ≅ ∠e′c′d′; translate point e′ to point b ∠acb ≅ ∠e′c′d′; translate point d′ to point b ∠abc ≅ ∠e′d′c′; translate point d′ to point a

1) ∠abc ≅ ∠e′d′c′; translate point e′ to point a
2) ∠acb ≅ ∠e′c′d′; translate point e′ to point b
3) ∠acb ≅ ∠e′c′d′; translate point d′ to point b
4) ∠abc ≅ ∠e′d′c′; translate point d′ to point a

Answer 1

To complete the proof, we reflect Δecd over segment ac to create a new triangle e′d′c′. Since the angle of reflection is equal to the angle of incidence, ∠e′d′c′ ≅ ∠abc. Therefore, the correct statement is 1) ∠abc ≅ ∠e′d′c′; translate point e′ to point a.

Step-by-step explanation:

To complete the proof, we need to determine which statement correctly establishes that ∠e′d′c′ ≅ ∠abc.

If we reflect Δecd over segment ac, we create a new triangle e′d′c′. Since the angle of reflection is equal to the angle of incidence, we have ∠e′d′c′ ≅ ∠abc. Therefore, the correct statement is 1) ∠abc ≅ ∠e′d′c′; translate point e′ to point a.