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Grade: 10
        
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.
2 months ago

Answers : (2)

Arun
24490 Points
							
Take the triangles as ABC and PQR
 
so
 
ab=pq
 
pr=ac
 
∠ a= ∠ p
 
∴ΔABC≅ΔPQR (sas congruence criterion )
 
hence proved
2 months ago
Aditya Gupta
2014 Points
							
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 :))
 
2 months ago
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