Class 10 Math Sample Paper 2019 | Q19B

This 2019 CBSE class 10 Maths 3 mark question is from Triangles. Solving this question requires the knowledge about Pythagoras theorem and medain of triangles. An easy 3 mark question in CBSE class 10 sample question paper. A standard NCERT text book question.

Question 19B: In ΔABC, if AD is the median, then show that AB² + AC² = 2(AD² + BD²)

Video Explanation

Explanatory Answer | CBSE 10th Math Sample Paper 2019 Question 19 Choice 2

AD is median, So BD = DC
By Pythagoras theorem,
In right triangle AEB, AB² = AE² + BE² .....(1)
In right triangle AEC, AC² = AE² + EC² .....(2)

Adding 1 and 2 on both sides of the equations,
AB² + AC² = 2 AE² + BE² + CE²
= 2 (AD² - ED²) + (BD - ED)2 + (DC + ED)2
= 2AD² - 2ED² + BD² + ED² - 2BD.ED + DC² + ED² + 2CD.ED
= 2AD² + BD² + CD²
= 2(AD² + BD²)