UDLA
7. In a squared sheet, draw two triangles of equal areas such that
(1) the triangles are congruent.
(ü) the triangles are not congruent.
ars?
Answers
Step-by-step explanation:
WER
(i) the triangles are congruent
△ABC≅△DEF
area(△ABC)=1×2+
2
1
×4=4sq. units
area(△DEF)=1×2+
2
1
×4=4sq. units
∴area(△ABC)=area(△DEF)
Thus, triangles are of equal areas and are congruent.
Perimeter:
As △ABC≅△DEF
By CPCT
AB=DE
BC=EF
AC=DF
Adding all the above 3, we get,
AB+BC+CA=DE+EF+FD
Perimeter of △ABC = Perimeter of △DEF
Thus, perimeters of congruent triangles are also equal.
(ii) the triangles are not congruent
△MNOnot≅△IJK
area(△MNO)=1×2+1×2=4sq. units
area(△IJK)=1×2+1×2=4sq. units
∴area(△MNO)=area(△IJK)
Thus, triangles are of equal areas and are congruent.
Perimeter:
Perimeter of △MNO = Perimeter of △IJK
Thus, perimeters of triangles are not equal.
Answered By
t
Answer:
Step-by-step explanation:
Given :-
→ ∆ABC ~ ∆DEF such that ar(∆ABC) = ar( ∆DEF) .
➡ To prove :- --------------
→ ∆ABC ≅ ∆DEF .
➡ Proof :-
→ ∆ABC ~ ∆DEF . ( Given ) .
Now, ar(∆ABC) = ar( ∆DEF ) [ given ] .
▶ From equation (1) and (2), we get
⇒ AB² = DE² , AC² = DF² , and BC² = EF² .
[ Taking square root both sides, we get ] .
⇒ AB = DE , AC = DF and BC = EF .
[ by SSS-congruency ] .
Hence, it is proved.