Respuesta :

Answer:

The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

[tex]\overline{AC} \perp \overline{BD}[/tex]

[tex]\overline{BD} \ bisects\ \overline{AC}[/tex]

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°( [tex]\overline{AC} \perp \overline{BD}[/tex] )}

AD ≅ CD              ....……….{ [tex]\overline{BD} \ bisects\ \overline{AC}[/tex] }

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

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ankitprmr2

Answer:

By SAS (Side-Angle-Side) concurrency rule.

[tex]\triangle ABD \cong \triangle CBD[/tex]

Step-by-step explanation:

Given:

[tex]\overline{AC} \perp \overline{BD}[/tex] and [tex]\overline{BD}\;\rm{ bisects}\; \overline{AC}[/tex]

To prove:

[tex]\bold{\triangle ABD \cong \triangle CBD}[/tex]

Solve,

In  ΔABD  and ΔCBD  

BD = BD    [BD is common side for both the triangles]

∠ADB = ∠CDB    [[tex]\overline{AC} \perp \overline{BD}[/tex], therefore the value of both the angles are of 90 degrees]

AD = CD          [[tex]\overline{BD}\;\rm{ bisects}\; \overline{AC}[/tex]]

Therefore,

By SAS (Side-Angle-Side) concurrency rule.

[tex]\triangle ABD \cong \triangle CBD[/tex]

For more information, please refer to the link:

https://brainly.com/question/7700137?referrer=searchResults

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