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In , , and . Another triangle is right-angled at such that and the hypotenuse…
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
,
∠
B
=
90
∘
\angle B = 90^\circ
∠
B
=
9
0
∘
,
A
B
=
9
cm
AB = 9\,\text{cm}
A
B
=
9
cm
and
B
C
=
40
cm
BC = 40\,\text{cm}
B
C
=
40
cm
. Another triangle
△
D
E
F
\triangle DEF
△
D
E
F
is right-angled at
E
E
E
such that
D
E
=
A
B
DE = AB
D
E
=
A
B
and the hypotenuse
D
F
=
A
C
DF = AC
D
F
=
A
C
. (a) Calculate the length of
A
C
AC
A
C
. (b) State, with reason, whether
△
A
B
C
\triangle ABC
△
A
B
C
and
△
D
E
F
\triangle DEF
△
D
E
F
are congruent. (c) Hence, find the length of
E
F
EF
E
F
.
Related theory
Pythagoras' Theorem
Triangle Properties
Triangle Congruence
Triangle Congruence Criteria
Additional congruence criteria (RHS)
Triangles
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