AIR MATH

Math Question

TN0025973_1 8 A partial proof is given, using isosceles triangle \( A B C \), where angle \( B \) is the vertex angle. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Statements } & \multicolumn{1}{|c|}{ Reasons } \\ \hline 1. Isosceles \( \triangle A B C \) & 1. Given \\ \hline 2. \( \overline{A B} \cong \overline{B C} \) & 2. Definition of an isosceles triangle \\ \hline \( 3 . \overline{B D} \) bisects \( \angle A B C \) & 3. Given \\ \hline \( 4 . \angle A B D \cong \angle C B D \) & 4. Definition of an angle bisector \\ \hline 5. & 5. \\ \hline \( 6 . \triangle A B D \cong \triangle C B D \) & 6. Side-Angle-Side (SAS) \\ \hline \end{tabular} Which statement and reason complete the proof? A. \( \overline{B D} \cong \overline{B D} \), Reflexive Property B. \( \overline{A D} \cong \overline{D C} \), Definition of a midpoint C. \( \angle A D B \cong \angle C D B \), All right angles are congruent. D. \( \angle A \cong \angle C \), Base angles of an isosceles triangle are congruent.

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