Math, asked by saketsorcerer, 1 year ago

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

Answers

Answered by kvnmurty

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

Mathexpert: It would be good to show images for these kind of answers. It will make the student understand better.

kvnmurty: thanks for suggestion. do u make diagrams ? have u seen how many i make.. no offence . it is a point i am clarifying

Mathexpert: I generally give a solution to a geometry question with a diagram only ...otherwise how can a child understands?

Mathexpert: It would be always good to give an answer with a diagram...in brainly ...you have an option to upload an image which supports your solution....that will make the child understand your solution better

Answered by Mathexpert

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 = $\frac{1}{2}* (\frac{1}{2} AC * BD)$

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

So,

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

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

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