Practice Proofs

Prove using SSS congruence.

\(\textbf{1)}\) Given: \( \overline{AB} \cong \overline{DE}\), \( \, \, C\) bisects \( \overline{AE} \) and \( \overline{BD} \)
Prove: \( \triangle ABC \cong \triangle EDC \)

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\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\( \overline{AC} \cong \overline{BD}\) \(C\) bisects \(\overline{AE}\) and \(\overline{BD}\)	Given
\( \overline{AC} \cong \overline{CE}\) \( \overline{BC} \cong \overline{CD}\)	Definition of Bisects
\(\triangle ABC \cong \triangle EDC\)	SSS triangle congruence

\(\textbf{2)}\) Given: \(ABDC\) is a parallelogram
Prove: \( \triangle ABC \cong \triangle DCB \)

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\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\(ABDC\) is a parallelogram	Given
\( \overline{AC} \cong \overline{BD}\) \( \overline{AB} \cong \overline{CD}\)	Definition of Parallelogram (opposite sides congruent)
\( \overline{BC} \cong \overline{CB}\)	Reflexive
\(\triangle ABC \cong \triangle DCB\)	SSS triangle congruence

\(\textbf{3)}\) Given: \( \overline{AB} \cong \overline{AC}\), \( \, \, \overline{AD}\) bisects \( \overline{BC} \)
Prove: \( \triangle ABD \cong \triangle ACD \)

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\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\( \overline{AB} \cong \overline{AC}\) \(\overline{AD}\) bisects \( \overline{BC} \)	Given
\( \overline{BD} \cong \overline{CD}\)	Definition of bisects
\( \overline{AD} \cong \overline{AD}\)	Reflexive
\(\triangle ABD \cong \triangle ACD\)	SSS triangle congruence

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