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Is right-angled at and
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
△
A
B
C
\triangle ABC
△
A
B
C
is right-angled at
C
C
C
and
A
C
=
B
C
AC = BC
A
C
=
B
C
. Let
C
D
CD
C
D
be the altitude from
C
C
C
to the hypotenuse
A
B
AB
A
B
. (i) Prove that
△
A
C
D
≅
△
B
C
D
\triangle ACD \cong \triangle BCD
△
A
C
D
≅
△
B
C
D
. (ii) Hence, show that
A
D
=
D
B
AD = DB
A
D
=
D
B
. (iii) What can you conclude about point
D
D
D
on the hypotenuse
A
B
AB
A
B
of
△
A
B
C
\triangle ABC
△
A
B
C
? State the result clearly.
Related theory
Quadrilaterals
Triangle Congruence
Triangle Congruence Criteria
Triangles
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