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Mathematics
Mathematics
Problem
In
△
P
Q
R
\triangle PQR
△
P
QR
,
P
Q
=
P
R
PQ = PR
P
Q
=
P
R
. Point
S
S
S
is taken on
Q
R
QR
QR
such that
P
S
⊥
Q
R
PS \perp QR
P
S
⊥
QR
. a. (i) Prove that
Q
S
=
S
R
QS = SR
QS
=
S
R
. b. (ii) Prove that
P
S
PS
P
S
bisects
∠
Q
P
R
\angle QPR
∠
QP
R
. c. (iii) If
∠
Q
P
R
=
64
∘
\angle QPR = 64^{\circ}
∠
QP
R
=
6
4
∘
, find
∠
Q
P
S
\angle QPS
∠
QP
S
.
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