given that ∠abc ≅ ∠dbe, which statement must be true?\n∠abc ≅ ∠abd\n∠abd ≅ ∠cbe\n∠cbd ≅ ∠dbe\n∠cbd ≅ ∠abc
given that ∠abc ≅ ∠dbe, which statement must be true?\n∠abc ≅ ∠abd\n∠abd ≅ ∠cbe\n∠cbd ≅ ∠dbe\n∠cbd ≅ ∠abc
Answer
Explanation:
Step1: Analyze angle - relationship
Since (\angle ABC\cong\angle DBE), we know that (\angle ABC=\angle ABD + \angle DBC) and (\angle DBE=\angle DBC+\angle CBE).
Step2: Use congruence property
If (\angle ABC=\angle DBE), then (\angle ABD+\angle DBC=\angle DBC + \angle CBE). By subtracting (\angle DBC) from both sides of the equation, we get (\angle ABD=\angle CBE), so (\angle ABD\cong\angle CBE).
Answer:
(\angle ABD\cong\angle CBE) (the second option)