Prove using SAS congruence.

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

Show Proof Steps

\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\(C\) bisects \( \overline{AE} \) and \( \overline{BD} \)	Given
\( \overline{AC} \cong \overline{CE}\) \( \overline{BC} \cong \overline{CD}\)	Definition of bisects
\(\angle ACB \cong \angle ECD\)	Vertical Angles
\(\triangle ACB \cong \triangle ECD\)	SAS triangle congruence

\(\textbf{2)}\) Given: \( \angle B \cong \angle C \), \( \, \, D\) bisects \( \overline{BC} \)
\(\,\,\,\,\,\,\,\,\,\)Prove: \( \triangle ABD \cong \triangle ACD \)
\(\,\,\,\,\,\,\,\,\,\)

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\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\( \angle B \cong \angle C \) Point \(D\) bisects \( \overline{BC} \)	Given
\(\overline{BD} \cong \overline{CD} \)	Definition of bisects
\(\overline{AB} \cong \overline{AC} \)	Base Angles Theorem
\(\triangle ABD \cong \triangle ACD\)	SAS triangle congruence

\(\textbf{3)}\) Given: \( \overline{AD} \cong \overline{AF}\), \( \, \, \overline{BD} \cong \overline{CF} \), \( \, \, E\) bisects \( \overline{DF} \)
\(\,\,\,\,\,\,\,\,\,\)Prove: \( \triangle DBE \cong \triangle FCE \)
\(\,\,\,\,\,\,\,\,\,\)

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\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\( \overline{AD} \cong \overline{AF}\) \(\overline{BD} \cong \overline{CF} \) \(E\) bisects \( \overline{DF} \)	Given
\(\angle D \cong \angle F\)	Isosceles Triangles Base Angles Theorem
\( \overline{DE} \cong \overline{FE}\)	Definition of bisects
\( \triangle DBE \cong \triangle FCE \)	SAS triangle congruence

Challenge Problem

\(\textbf{4)}\) Given: \(ABDC\) is a parallelogram
\(\,\,\,\,\,\,\,\,\,\)Prove: \( \triangle ABC \cong \triangle DCB \)
\(\,\,\,\,\,\,\,\,\,\)

Show Proof Steps

\(\underline{\text{Statement}}\)	\(\underline{\text{Reason}}\)
\(ABDC\) is a parallelogram	Given
\(\overline{AC} \cong \overline{BD} \) \(\overline{AB} \cong \overline{CD} \)	Opposite sides congruent in a parallelogram
\(\angle A \cong \angle D\)	Opposite angles congruent in a parallelogram
\(\triangle ABC \cong \triangle DCB\)	SAS triangle congruence

See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Proving Triangle Congruence SAS}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Proving Triangle Congruence SSS}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Proving Triangle Congruence ASA}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Proving Triangle Congruence AAS}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Proving Triangle Congruence CPCTC}\)
\(\,\,\,\,\,\,\,\,\text{Corresponding Parts of Congruent Triangles are}\)\(…\)