Question

In the given figure, AD is the median A ABC. Prove that ar triangle ( ABD) = ar triangle ( ACD).

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Answer 1

Given: AD is the median of the triangle ABC.

To find:  Prove that area of triangle (ABD) = area of triangle ( ACD).

Solution:

• As we have given two triangles, ABD and ACD, so lets consider them.

• In triangle ABD and triangle ACD, we have:

              ang ADB = ang ADC ..............(each of 90°)

              AD = AD ...........(common)

              ang BAD = ang DAC ...............(median divides the angle in two equal parts)

• So by SAS rule:

             triangle ABD ≅ triangle ACD

• So area is also equal, and also we know that median divides the triangle in two equal area.
• So the median AD divides the triangle ABC in two equal parts.

Answer:

            Hence, area of triangle  ( ABD) = area of triangle ( ACD).