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Standard IX
Mathematics
SAS Criteria for Congruency
Question
In
Δ
A
B
C
and
Δ
D
E
F
, AB = DF and
∠
A
=
∠
D
. The two triangles will be congruent by SAS axiom if :
AC = DE
BC = EF
AC = EF
BC = DE
A
BC = EF
B
BC = DE
C
AC = DE
D
AC = EF
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Solution
Verified by Toppr
For triangle to be congruent
S
A
S
(Side angle Side) axiom we need to have two equal sides and the included angle same.
In
Δ
A
B
C
and
Δ
D
F
E
We have
A
B
=
D
F
and
∠
A
=
∠
D
But
∠
A
is formed by the two sides AB and AC of
Δ
A
B
C
But
∠
D
is formed by the two sides DE and DF of
Δ
D
F
E
So we need
A
C
=
D
E
for the two triangles to be congruent.
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Similar Questions
Q1
In ∆ABC and ∆DEF, AB = DF and ∠A = ∠D. The two triangles will be congruent by SAS axiom if:
View Solution
Q2
Question 11
In
Δ
A
B
C
and DEF, AB =FD and
∠
A
=
∠
D
. The two triangles will be congruent by SAS axiom, if
(A) BC = EF
(B) AC = DE
(C) AC = EF
(D) BC = DE
View Solution
Q3
Question 11
In
Δ
A
B
C
and DEF, AB =FD and
∠
A
=
∠
D
. The two triangles will be congruent by SAS axiom, if
(A) BC = EF
(B) AC = DE
(C) AC = EF
(D) BC = DE
View Solution
Q4
In
Δ
A
B
C
and
Δ
D
E
F
,
A
B
=
D
F
and
∠
A
=
∠
D
. The two triangles will be congruent by SAS
axiom if :
View Solution
Q5
In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom, if __________.