The congruence theorem that can be used to prove △BAE ≅ △CAD isA. SSS. B. ASA.C. SAS. D. HL.

Answer:Option is D.The congruence theorem that can be used to prove  △BAE ≅ △CAD  is HL (Hypotenuse and leg of a right triangle.)Step-by-step explanation:From the Figure:Consider  △BAE ≅ △CAD ∴ [tex]\angle BAE=\angle DAC=90^{\circ}[/tex] [tex]BE=CD \left \{ Hypotenuse side\right \}[/tex][tex]BA=AC \left \{One leg of the triangle are equal\right \}[/tex]Therefore, by HL i.e, (Hypotenuse and leg of a right triangle) which implies that two right angle triangle are congruent if their hypotenuse and one corresponding leg of the triangle are equal.Hence,  [tex]\bigtriangleup BAE\simeq \bigtriangleup CAD[/tex] by HL congruence theorem.