if ABC is a triangle right angled at B and m n are the midpoints of Ab and BC then 4 into n square + c m square equals to what
Answers
Answer:
4(AN² + CM²) = 5AC²
Step-by-step explanation:
if ABC is a triangle right angled at B and m n are the midpoints of Ab and BC then 4 into (an square + c m square equals) to what
m & n are mid points of AB & BC
AM = BM = AB/2
BN + CN = BC/2
CM² = BM² + BC²
=> CM² = (AB/2)² + BC²
=> CM² = (AB)²/4 + BC²
AN² = AB² + BN²
=> AN² = AB² + (BC/2)²
=> AN²= AB² + BC²/4
4(AN² + CM²)
= 4 (AB² + BC²/4 + (AB)²/4 + BC²)
= 4AB² + BC² + AB² + 4BC²
= 5AB² + 5BC²
= 5AC²
4(AN² + CM²) = 5AC²
Answer:
Given, △ABC, M is mid point of AB and N is mid point of BC.
In △ABN,
AN
2
=AB
2
+BN
2
(Pythagoras Theorem)
AN
2
=AB
2
+(
2
BC
)
2
....(1)
In △BMC,
MC
2
=BM
2
+BC
2
(Pythagoras Theorem)
MC
2
=BC
2
+(
2
AB
)
2
....(2)
Add (1) and (2),
AN
2
+MC
2
=AB
2
+(
2
BC
)
2
+BC
2
+(
2
AB
)
2
AN
2
+MC
2
=
4
5
AB
2
+
4
5
BC
2
4(AN
2
+MC
2
)=5(AB
2
+BC
2
)
4(AN
2
+MC
2
)=5AC
2
(Pythagoras Theorem in △ABC)
Step-by-step explanation: