Math  /  Geometry

QuestionGiven BD,ABED\angle \mathrm{B} \cong \angle \mathrm{D}, \overline{A B} \cong \overline{E D} Prove ABCEDC\triangle A B C \cong \triangle E D C \begin{tabular}{c|l} Statements & \multicolumn{1}{c}{ Reasons } \\ \hline 1. BD,ABED\angle \mathrm{B} \cong \angle \mathrm{D}, \overline{A B} \cong \overline{E D} & 1. Given \\
2. ACBECD\angle \mathrm{ACB} \cong \angle \mathrm{ECD} & 2\mathbf{2} \\
3. ABCEDC\triangle A B C \cong \triangle E D C & 3. \end{tabular}

Given EFHG,HEFG\overline{E F}||\overline{H G}, \overline{H E}|| \overline{F G} Prove HEFFGH\triangle H E F \cong \triangle F G H F{ }^{F}
How can you prove that ABCADC\triangle A B C \cong \triangle A D C ? \begin{tabular}{l|l} \multicolumn{1}{c|}{ Statements } & \multicolumn{1}{c}{ Reasons } \\ \hline 1. EFIIG,HEFG\overline{\mathrm{EF}}\|\mathrm{IIG}, \overline{\mathrm{HE}}\| \overline{\mathrm{FG}} & 1. Given \\
2. HFFH\overline{H F} \cong \overline{F H} & 2\mathbf{2}. \\
3. EFHGHF\angle \mathrm{EFH} \cong \angle \mathrm{GHF}, & 3\mathbf{3}. \\ EHFGFH\angle \mathrm{EHF} \cong \angle \mathrm{GFH} & 4.\mathbf{4 .} \end{tabular} \begin{tabular}{l|l} \multicolumn{2}{c|}{ Statements } \\
1. & \multicolumn{1}{c}{ Reasons } \\ \hline 2. & 1. \\
3. & 2. \\
3. & \end{tabular} 3.

Studdy Solution
The triangles ABC\triangle ABC and EDC\triangle EDC are congruent by the **ASA Congruence Criterion**.

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