Math  /  Geometry

QuestionGiven: A\angle A and C\angle C are right angles; ABCD\overline{A B} \cong \overline{C D}. Prove: ABDCDB\triangle A B D \cong \triangle C D B Complete the proof. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statements } & \multicolumn{1}{c|}{ Reasons } \\ \hline \begin{tabular}{l}
1. A\angle A and C\angle C are \\ right angles; ABCD\overline{A B} \cong \overline{C D}. \end{tabular} & 1. \\ \hline \begin{tabular}{c}
2. ABD\triangle A B D and CDB\triangle C D B are \\ right triangles. \end{tabular} & 2. \\ \hline 3. BDDB\overline{B D} \cong \overline{D B} & 3. \\ \hline 4. ABDCDB\triangle A B D \cong \triangle C D B & 4. \\ \hline \end{tabular}

Drag the reasons to the correct order. (i) Instructions
LL Theorem
Definition of right triangle
Reflexive Property of Congruence
Given
Symmetric Property of Congruence HL Theorem

Studdy Solution
Apply a congruence theorem to prove triangle congruence:
4. ABDCDB\triangle A B D \cong \triangle C D B
Reason: HL Theorem
The proof is complete.

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