Question

Given: m∠A = m∠C = 90° AB ║ DC Prove: ∆ABD ≅ ∆CBD

Answer 1

Answer:

Angle-Angle-Side (AAS)

Step-by-step explanation:

Given triangles; ΔABD and ΔCBD

  <A = <C = $90^{0}$ (right angle property)

   AB ║ DC (given)

Then,

    DA ║ CB

   <B ≅ <D (congruent property)

    DB ≅ BD (similarity property)

    <D + <B = <B + <D (complementary angles, and property of triangles)

Therefore by Angle-Angle-Side (AAS),

                 ∆ABD ≅ ∆CBD