Example:
If ∠A and ∠B are acute angles such that tan A = tan B
then prove ∠A = ∠B.
Proof:
Consider ΔAMN and ΔBPQ in which ∠M = ∠P = 90º,
∠A and ∠B are acute.
tan A = tan B
[Given]
A
M
N
B
P
Q
MN
AM
tan A =
PQ
BP
tan B =
=
MN
AM
PQ
BP
∴
...(i)
=
MN
PQ
AM
BP
ΔAMN ~ ΔBPQ
…(i)
=
MN
PQ
AM
BP
Example:
If ∠A and ∠B are acute angles such that tan A = tan B
then prove ∠A = ∠B.
Proof:
A
M
N
B
P
Q
=
MN
PQ
AM
BP
∠M
[From (i)]
=
∠P
[Each 90º]
∴
In ΔAMN and ΔBPQ,
[By SAS similarity criterion]
∴
[Corresponding angles of
similar triangles]
∠A
=
∠B