Area triangle theorem prove it
Answers
Answer:
H Siam भी man's जंक्शन ms
Step-by-step explanation:
H the first 6 of the whole body of female group of men in the morning and night as they were
By the police and the police were arrested and arrested by the police to help the police to be a friend
:-
ANSWER
Area Theorem : The ratio of areas of two similar triangles is equal to the squares of the ratio of their corresponding sides.
Given, △ABD∼△PQR
∴∠A=∠P, ∠B=∠Q, and ∠C=∠R
PQ
AB
=
QR
BC
=
PR
CA
.......(1)
The ratio of area of △ABD and △PQR is given as,
ar(△PQR)
ar(△ABC)
=
2
1
×QR×PS
2
1
×BC×AD
ar(△PQR)
ar(△ABC)
=
QR
BC
×
PS
AD
........(2)
In △ABD and △PQS
∠B=∠Q [Given]
∠ADB=∠PSQ [Each 90
o
]
∴△ABD∼△PQS [AA similarity]
⇒
PS
AD
=
PQ
AB
=
QS
BD
.......(3) [Corresponding sides are proportional]
From (1) and (3), we get
PQ
AB
=
QR
BC
=
PR
CA
=
PS
AD
QR
BC
=
PS
AD
From (2) and (4), we get
ar(△PQR)
ar(△ABC)
=
QR
BC
×
QR
BC
=
QR
2
BC
2
∴
ar(△PQR)
ar(△ABC)
=
PQ
2
AB
2
=
QR
2
BC
2
=
PR
2
CA
2