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secondary 4 | A Maths
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Date Posted: 3 years ago
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A) to show angle bisection:
Show both angles are equal:
(ABL = LBC)
Let angle LBC be x
Then BLC = 180 - 90 - x (angles in triangle BCL)
= 90 - x
Angle ALN = BLC (vertically opp angle)
Since AL = AN,
angle ANL = ALN (isosceles triangle LAN)
angle BAN = 90 (radius perpend to tangent )
:. Angle ABL = 180 - 90 - (90-x)
(angles in triangle BAN)
= x
= angle LBC (shown) //
B) Angle BOL = Angle BAN (Corr angle)
= Angle BCL (both 90 deg)
Angle OBL = Angle CBL (from part A)
BL = BL (exact same length)
By AAS test, they are congruent //
Show both angles are equal:
(ABL = LBC)
Let angle LBC be x
Then BLC = 180 - 90 - x (angles in triangle BCL)
= 90 - x
Angle ALN = BLC (vertically opp angle)
Since AL = AN,
angle ANL = ALN (isosceles triangle LAN)
angle BAN = 90 (radius perpend to tangent )
:. Angle ABL = 180 - 90 - (90-x)
(angles in triangle BAN)
= x
= angle LBC (shown) //
B) Angle BOL = Angle BAN (Corr angle)
= Angle BCL (both 90 deg)
Angle OBL = Angle CBL (from part A)
BL = BL (exact same length)
By AAS test, they are congruent //
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