Practice Proofs
Prove using SSS congruence.
\(\textbf{1)}\) Given: \( \overline{AB} \cong \overline{DE}\), \( \, \, C\) bisects \( \overline{AE} \) and \( \overline{BD} \)
Prove: \( \triangle ABC \cong \triangle EDC \)
\(\underline{\text{Statement}}\)
\(\underline{\text{Reason}}\)
\( \overline{AC} \cong \overline{BD}\)
\(C\) 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
| \(\underline{\text{Statement}}\) | \(\underline{\text{Reason}}\) |
|---|---|
\(C\) bisects \(\overline{AE}\) and \(\overline{BD}\) |
|
\( \overline{BC} \cong \overline{CD}\) |
|
\(\textbf{2)}\) Given: \(ABDC\) is a parallelogram
Prove: \( \triangle ABC \cong \triangle DCB \)
\(\underline{\text{Statement}}\)
\(\underline{\text{Reason}}\)
\(ABDC\) 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
| \(\underline{\text{Statement}}\) | \(\underline{\text{Reason}}\) |
|---|---|
\( \overline{AB} \cong \overline{CD}\) |
(opposite sides congruent) |
\(\textbf{3)}\) Given: \( \overline{AB} \cong \overline{AC}\), \( \, \, \overline{AD}\) bisects \( \overline{BC} \)
Prove: \( \triangle ABD \cong \triangle ACD \)
\(\underline{\text{Statement}}\)
\(\underline{\text{Reason}}\)
\( \overline{AB} \cong \overline{AC}\)
\(\overline{AD}\) 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
| \(\underline{\text{Statement}}\) | \(\underline{\text{Reason}}\) |
|---|---|
\(\overline{AD}\) bisects \( \overline{BC} \) |
|
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