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If two triangles have two sides of one equal to two sides of another and the included angles are supplementary, prove that they are equal in area.

If two triangles have two sides of one equal to two sides of another and the included angles are supplementary, prove that they are equal in area.

Grade:10

3 Answers

Arun
25750 Points
4 years ago
Take the triangles as ABC and PQR
 
so
 
ab=pq
 
pr=ac
 
∠ a= ∠ p
 
∴ΔABC≅ΔPQR (sas congruence criterion )
 
hence proved
Aditya Gupta
2081 Points
4 years ago
note that aruns ans is once again wrong, non sensical and poorly understood.
he doesnt even understand the meaning of supplementary angles.
let triangles be ABC and PQR.
given AB= PQ
AC= PR
and the included angles are supplementary implies that they add up to 180.
so that angle BAC + angle QPR= 180
or angle QPR= 180 – angle BAC
now, we use the following formula for area:
area of ABC= ½ AB*AC*sin(angle BAC) (note that the proof of this formula is easy and can be found online)
and area of PQR= ½ PQ*PR*sin(angle QPR)= ½ AB*AC*sin(180 – angle BAC)= ½ AB*AC*sin(angle BAC).
hence, area of ABC= area of PQR.
KINDLY APPROVE :))
 
debangshu Mandal
22 Points
2 years ago
I think arun is 9th fail student he even does not know the meaning of supplymebtary he should study class9 again 

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