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The missing statement in the proof specified is given by: Option B: ∠BCA≅∠DCB
What is the reflexive property of congruence?
According to the reflexive feature of congruence, the geometric quantity under consideration—be it an angle, a line segment, a form, etc.—is congruent to itself.
The third step's key concept in this instance is the "Reflexive Property of Congruence."
The fourth phase comes to the conclusion that the ΔABC~ΔBDC criteria for similarity are met.
Since it was established in the second stage that ∠ABC≅∠BDC
Therefore, in order for the fourth step to apply angle-angle similarity, which requires the angles of two considered triangles to be congruent, we must demonstrate another angle pair of triangles ΔABC and ΔBDC being congruent in the third step.
Internal angle C is the common angle in the triangles ABC and BDC.
As a result, it is consistent with itself due to its reflexive characteristic.
We obtain the following notation for internal angle C from triangle ABC:
Angle ACB and BCA(both will work)
Triangle BDC gives us the following notation for internal angle C:
Angle DCB and BCD(Both will function.)
They fit together. The second choice takes angle C into account, so:
∠BCA≅∠DCB (second option) is the missing statement.
Learn more about the reflexive property of congruency here:
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