Question

Given: \overline{AC} \perp \overline{BD} AC ⊥ BD and \overline{BD} BD bisects \overline{AC}. AC . Prove: \triangle ABD \cong \triangle CBD△ABD≅△CBD.

Answer 1

Answer:

The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

$\overline{AC} \perp \overline{BD}$

$\overline{BD} \ bisects\ \overline{AC}$

AD = CD      .........BD bisect AC

To Prove:

△ABD ≅ △CBD

Proof:

In  ΔABD  and ΔCBD  

BD ≅ BD              ....……….{Reflexive Property}

∠ADB ≅ ∠CDB    …………..{Measure of each angle is 90°( $\overline{AC} \perp \overline{BD}$ )}

AD ≅ CD              ....……….{ $\overline{BD} \ bisects\ \overline{AC}$ }

ΔABD  ≅ ΔCBD   .......….{By Side-Angle-Side Congruence test}  ...Proved