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

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

Step-by-step explanation:

Given:

and

To prove:

Solve,

In  ΔABD  and ΔCBD  

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

∠ADB = ∠CDB    [, therefore the value of both the angles are of 90 degrees]

AD = CD          []

Therefore,

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

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The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

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°( )}

AD ≅ CD              ....……….{ }

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

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq