Question

ABC is a right angle triangle at b if d and e are midpoints of sides BC CA and ab respectively prove that a b square + c square is equals to 5 de square

Answer 1

Answer:Given: A right triangle ABC, right angled at C. D and E are points on sides AC and BC

respectively.

To Prove : AE2 + BD2 = AB2 + DE? = Const: Join AE, BD and DE.

Proof: In AACE AE? = AC2 + CE2 ..(1)

[Using Pythagoras theorem] In ABCD, BD2 = CD2 + BC2 ..(ii)

[Using Pythagoras theorem]

Adding (i) and (ii), we get AE? + BD? = (AC2 + BC?) + (CE? + CD²) AE? + BD2 = AB² + DE? Hence Proved.

Step-by-step explanation:

Answer 2

Answer:Given: A right triangle ABC, right angled at C. D and E are points on sides

AC and BC

respectively.

To Prove : AE2 + BD2 = AB2 + DE? = Const: Join AE, BD and DE.

Proof: In AACE AE? = AC2 + CE2 ..(1) =

[Using Pythagoras theorem] In ABCD,

BD2 = CD2 + BC2 ..(ii)

[Using Pythagoras theorem]

[Using Pythagoras theorem] In ABCD, BD2 = CD2 + BC2 ..(ii)

[Using Pythagoras theorem]

Adding (i) and (ii), we get AE? + BD? = (AC2 + BC?) + (CE? + CD2) AE? + BD2 = AB? + DE? Hence Proved.