Question

M and n are the mid points of sides qr and pq respectively of a triangle pqr right angled at q prove that:
1)PMSQUARE +RN SQUARE =5 MNSQUARE
2)4RN SQUARE =4PQ SQUARE +QR SQAURE

3)4RN SQUARE =PQSQUARE +4QR SQUARE

4)4 (PMSQUARE +RNSQUARE)=5PRSQUARE.





PLS TELLL FAST ....I WANT HELP...ILLL MARY U EITH 30 POINTS

Answer 1

Answer:

Step-by-step explanation:

4(PM² + RN²)  = 5PR²

Step-by-step explanation:

data given is not complete

let assume , we have to To Prove

4 (p m square + r n square)  = 5 pr²

Given :

M and n are the midpoints of sides QR and PQ respectively

PM² =  PQ² + QM²

=> PM² = PQ² + (QR/2)²

=> PM² = PQ² + QR²/4

=> 4PM² = 4PQ² + QR²

Similarly

RN² = QR² + QN²

=> RN² = QR² + (PQ/2)²

=> 4RN² = 4QR² + PQ²

Adding both

4PM²  +  4RN² = 4PQ² + QR² + 4QR² + PQ²

=> 4(PM² + RN²)  = 5(PQ² + QR²)

=> 4(PM² + RN²)  = 5PR²

Answer 2

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