NCERT Solutions for Class 10 Maths Chapter 6

Important NCERT Questions

Triangles

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 6.5

Page No:151

Questions No:13

# D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE² + BD² = AB²+ DE².

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In ΔACE, by pythagoes thoeorem

AC² + CE² AE² …(1)

In ΔBCD, by Pythagoras theorem

BC² + CD² = DB² …(2)

From the equation (1) and (2), we have

AC² + CE² + BC² + CD² = AE² + DB ² …(3)

In ΔBCD, by pythagoras theorem

DE² = CD² + CE² …(4)

In ΔABC, by pythagoras theorem

AB² = AC² + CB² …(5)

From the equation (3), (4) and (5), we have

DE² + AB² = AE² + DB²