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Singapore Senior Math Olympiad
2008 Singapore Senior Math Olympiad
1
1
Part of
2008 Singapore Senior Math Olympiad
Problems
(1)
equal angles lead to equal angles inside a trapezium
Source: Singapore Senior 2008
7/10/2019
Let
A
B
C
D
ABCD
A
BC
D
be a trapezium with
A
D
/
/
B
C
AD // BC
A
D
//
BC
. Suppose
K
K
K
and
L
L
L
are, respectively, points on the sides
A
B
AB
A
B
and
C
D
CD
C
D
such that
∠
B
A
L
=
∠
C
D
K
\angle BAL = \angle CDK
∠
B
A
L
=
∠
C
DK
. Prove that
∠
B
L
A
=
∠
C
K
D
\angle BLA = \angle CKD
∠
B
L
A
=
∠
C
KD
.
geometry
trapezium
trapezoid
equal angles