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Byju's Answer
Standard IX
Mathematics
SSS Similarity
In ΔABC, AB =...
Question
In
Δ
A
B
C
, AB = AC and AD is the median. Then by which similarity are the
Δ
A
D
B
and
Δ
A
D
C
similar?
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Solution
In the triangles
Δ
ADB and
Δ
ADC,
AD is the common side
BD = DC [Since D is the midpoint of BC]
AB = AC [Given]
So, ratio of corresponding sides is
A
D
A
D
=
B
D
D
C
=
A
B
A
C
=
1
Therefore the triangles are similar by SSS similarity.
But SSS is not in the given option
So, In the triangles
Δ
ADB and
Δ
ADC:
AB = AC [Given]
∠
B
=
∠
C
[Since AB = AC, angles opposite to equal sides are equal]
BD = DC [Since D is the midpoint of BC]
Therefore the triangles are similar by SAS similarity.
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