If the area of two similar triangle are equal ,prove that they are congruent.
Answers
Answered by
1
Step-by-step explanation:
Given that:
ar△ABC=ar△DEF
Prove that:
△ABC≅△DEF
Proof:
Two triangles ABC and DEF are shown in figure.
ar△ABC=ar△DEF (given)
ar△DEF
ar△ABC
=1
DE
2
AB
2
=
EF
2
BC
2
=
FD
2
CA
2
=1 [ USING THEOREM OF AREA OF SIMILAR TRIANGLES]
AB=DE,BC=EF,CA=FD
Thus, △ABC≅△DEF [BY SSS criterion of congruence
Answered by
1
Step-by-step explanation:
Data: △ABC∼△DEF
ar(△ABC)=ar(△DEF)
To Prove: △ABC≅△DEF
Proof:
ar(△DEF)
ar(△ABC)
=
DE
2
AB
2
=
EF
2
BC
2
=
FD
2
CA
2
[∵ Theorem of areas of similar triangles]
1=
DE
2
AB
2
=
EF
2
BC
2
=
FD
2
CA
2
[∵ By data areas are equal]
⇒AB
2
=DE
2
∴AB=DE
BC
2
=EF
2
∴BC=EF
CA
2
=FD
2
∴CA=FD
∴△ABC≅△DEF [∵ SSS]
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