Which of the following completes the proof?
Triangles ABC and EDC are formed from segmen...
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Mathematics, 26.02.2020 03:57, courtnicollee
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, translate point E' to point A. This establishes that . Therefore, ΔACB ~ ΔECD by the AA similarity postulate.
∠ABC ≅ ∠E'D'C'; ∠E'D'C' ≅ ∠ABC
∠ACB ≅ ∠E'C'D'; ∠D'E'C' ≅ ∠BAC
∠ACB ≅ ∠E'C'D'; ∠E'D'C' ≅ ∠ABC
∠ABC ≅ ∠E'D'C'; ∠D'E'C' ≅ ∠BAC
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