[tex]AC\perp BD[/tex]
Reason: Given
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[tex]\angle BDC_{\text{ }}and_{\text{ }}\angle BDA_{\text{ }}are_{\text{ }}right_{\text{ }}angles[/tex]
Reason: Perpendicular lines form right angles.
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[tex]\angle BDC\cong\angle BDA[/tex]
Reason: All right angles are congruent.
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[tex]CD\cong AD[/tex]
Reason: Given
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[tex]BC\cong BA[/tex]
Reason: Given
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[tex]\begin{gathered} \Delta ABD\cong CBD \\ \end{gathered}[/tex]
Reason: HL
