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Byju's Answer
Standard VII
Mathematics
AAS Criteria for Congruency
a In the give...
Question
(a) In the given figure, prove that:
(i)
Δ
A
B
C
≅
Δ
D
C
B
(ii) AC = DB
(b) In the figure, it is given that
∠
A =
90
∘
, AB = AC, and D is the mid point of BC. Find
∠
ADC.
[4 MARKS]
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Solution
Each Part: 2 Marks
(a)
(i) In
Δ
A
B
C
and
Δ
D
C
B
A
B
=
D
C
[Given]
∠
A
B
C
=
∠
D
C
B
=
90
∘
[Given]
B
C
=
B
C
[Common side]
⇒
Δ
A
B
C
≅
Δ
D
C
B
[SAS congruency criteria]
(ii)
∴
A
C
=
D
B
[Corresponding parts of congruent triangles]
(b)
AB = AC (Given)
BD = DC (D is mid point of BC)
AD = AD (Common side)
Therefore,
△
ADB
≅
△
ADC [SSS congruency criteria]
thus,
∠
ADB =
∠
ADC (c.p.c.t.) ...(1)
but,
∠
ADB +
∠
ADC =
180
∘
[linear pair]
∴
∠
ADC +
∠
ADC =
180
∘
⇒
2
∠
ADC =
180
∘
⇒
∠
A
D
C
=
180
°
2
⇒
∠
A
D
C
=
90
°
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2
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