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Let us take the two triangles  ΔBDA and ΔBDC. These two are congruent as:

DA = DC (as BD is bisecting AC), DB is common, and the
                 Angle BDA = angle BDC = 90  (BD perpendicular to AC)

So It is easy now that:  angle DBA = angle DBC

Since their sum is the angle ABC = 90 deg (given),

   Hence      angle DBC  = 1/2 angle ABC. = 45 deg.

Ratio = 1/2

It would be good to show images for these kind of answers. It will make the student understand better.
thanks for suggestion. do u make diagrams ? have u seen how many i make.. no offence . it is a point i am clarifying
I generally give a solution to a geometry question with a diagram only ...otherwise how can a child understands?
It would be always good to give an answer with a brainly have an option to upload an image which supports your solution....that will make the child understand your solution better
The Brainliest Answer!
Area of triangle ABC =  \frac{1}{2}* AC * BD

Area of triangle BDC =   \frac{1}{2}* CD * BD

Area of triangle BDC =  \frac{1}{2}*  \frac{1}{2} AC * BD

Area of triangle BDC =  \frac{1}{2}* (\frac{1}{2} AC * BD)

Area of triangle BDC =  \frac{1}{2}* (Area of \Delta ABC)


 \frac{Ar( \Delta BDC)}{Ar(\Delta ABC)} =  \frac{1}{2}

The ratio of areas of triangles BDC and ABC is equal to 1 : 2

1 5 1