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Mathematics
Mathematics
Problem
Two triangles
△
A
B
C
\triangle ABC
△
A
B
C
and
△
P
Q
R
\triangle PQR
△
P
QR
are such that
∠
B
=
90
∘
\angle B = 90^\circ
∠
B
=
9
0
∘
,
∠
Q
=
90
∘
\angle Q = 90^\circ
∠
Q
=
9
0
∘
,
A
B
=
P
Q
=
6
cm
AB = PQ = 6\,\text{cm}
A
B
=
P
Q
=
6
cm
,
A
C
=
P
R
=
10
cm
AC = PR = 10\,\text{cm}
A
C
=
P
R
=
10
cm
and
B
C
=
8
cm
BC = 8\,\text{cm}
B
C
=
8
cm
. a. (i) Prove that
△
A
B
C
≅
△
P
Q
R
\triangle ABC \cong \triangle PQR
△
A
B
C
≅
△
P
QR
. b. (ii) Hence find the length of
Q
R
QR
QR
. c. (iii) If
∠
C
=
40
∘
\angle C = 40^\circ
∠
C
=
4
0
∘
, find
∠
R
\angle R
∠
R
. State the reason for your answer.
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