# ABC is a right triangle right angled at B. BD is perpendicular bisector of AC. Find ratio of ar(DBC) and ar(abc). Relate this answer to triangles chapter

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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

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

The Brainliest Answer!

Area of triangle BDC = .

Area of triangle BDC =

Area of triangle BDC =

So,

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