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In , it is given that . A point lies on such that . Answer the…
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
, it is given that
A
B
=
A
C
AB = AC
A
B
=
A
C
. A point
D
D
D
lies on
B
C
BC
B
C
such that
A
D
⊥
B
C
AD \perp BC
A
D
⊥
B
C
. Answer the following: (i) Prove that
△
A
B
D
≅
△
A
C
D
\triangle ABD \cong \triangle ACD
△
A
B
D
≅
△
A
C
D
. (ii) Hence, show that
B
D
=
D
C
BD = DC
B
D
=
D
C
. (iii) State what
A
D
AD
A
D
does to base
B
C
BC
B
C
of
△
A
B
C
\triangle ABC
△
A
B
C
, giving one reason drawn from your proof above.
Related theory
Quadrilaterals
Triangle Congruence
Triangle Congruence Criteria
Additional congruence criteria (RHS)
Triangles
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