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Given: AB ≅ BC and D is the midpoint of AC. Prove: BD bisects ∠ ABC. Step Statement Reason 1 AB ≅ BC Given 2 D is the midpoint of AC 3 ∠ ABD ≅∠ CBD Corresponding Parts of Congruent Triangles are Congruent (CPCTC) 4 BD bisects ∠ ABC A segment that divides a larger angle into two congruent angles bisects that larger angle 5 AD ≅ DC A midpoint divides a segment into two congruent segments 6 BD ≅ BD Reflexive Property 7 ABD ≅ CBD SSS
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