It is proved that [tex]\rm \overline{BD} \cong \overline{CA}[/tex] by using the given data and also by using base angle theorem, reflexive property, and SAS postulate.
Given :
- ABCD is a trapezoid.
- [tex]\rm \overline{BA} \cong \overline{CD}[/tex]
The following statements with reasons are given below to prove that [tex]\rm \overline{BD} \cong \overline{CA}[/tex].
Statement Reasons
ABCD is a trapezoid Given
[tex]\rm \overline{BA} \cong \overline{CD}[/tex] Given
Trapezoid ABCD is isosceles trepezoid. According to the definition.
[tex]\rm \angle BAD \cong \angle CDA[/tex] According to base angle theorem.
[tex]\rm \overline{BD} \cong \overline{CA}[/tex] According to reflexive property.
[tex]\rm \Delta BAD \cong \Delta CDA[/tex] Side Angle Side postulate.
[tex]\rm \overline{BD} \cong \overline{CA}[/tex] CPCTC
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https://brainly.com/question/1593616
