M and N are mid- point on sides QR and PQ respectively of `/_\ PQR`, right-anggled at Q. Prove that :
`PM^(2)+RN^(2)= 5 MN^(2)`.

M and N are mid point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : 4PM^(2)= 4PQ^(2)+QR^(2) .

M and N are point on sides QR and PQ respectively of /_\ PQR , right-angled at Q. Prove that : PM^(2)+RN^(2)=PR^(2)+MN^(2)

M and N are the mid-points of the sides QR and PQ respectively of a DeltaPQR , right-angled at Q. Prove that : (i) PM^(2)+RN^(2)=5MN^(2) (ii) 4PM^(2)=4PQ^(2)+QR^(2) (iii) 4RN^(2)=PQ^(2)+4QR^(2) (iv) 4(PM^(2)+RN^(2))=5PR^(2)

P and Q are points on the sides C A and C B respectively of A B C , right-angled at C . Prove that A Q^2+B P^2=A B^2+P Q^2 .

In Figure, Pa n dQ are the midpoints of the sides C Aa n dC B respectively of A B C right angled at C. Prove that 4(A Q^2+B P^2)=5A B^2 .

P and Q are the mid-points of the CA and CD respectively of a triangle ABC, right angled at C. Prove that: 4AQ^2 = 4AC^2 + BC^2 , 4BP^2 = 4BC^2 + AC^2 , and 4(AQ^2 + BP^2) = 5AB^2 .

M and N are points on sides AC and BC respectively of a triangleABC . State whether MN||BA if CM = 4.2 cm, MA= 2.8 cm , NB = 3.6 cm, CN = 5.7 cm.

In triangle ABC, the medians BP and CQ are produced upto points M and N respectively such that BP=PM and CQ=QN . Prove that : A is the mid-point of MN.

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

In A P Q R , if P Q=QR\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ P R\ a n d\ R P respectively. Prove that L N=M N