Thread: Proving two bisectors are equal

In a triangle ABC, angle B is 60 degrees. Angles A and C are bisected to points D and E respectively, on the edge of the triangle (see diagram). They cross at point O. Prove that OD = OE



I've gone through it a little and got this.

2x + 2y + 60 = 180
2x + 2y = 120
x + y = 60

I don't know if this helps at all.

Remember, angles A and C are bisected, so the two adjacent angles are equal to each other (x, x and y, y)

Thanks for any help, BG

Hello BG5965

Originally Posted by BG5965

In a triangle ABC, angle B is 60 degrees. Angles A and C are bisected to points D and E respectively, on the edge of the triangle (see diagram). They cross at point O. Prove that OD = OE



I've gone through it a little and got this.

2x + 2y + 60 = 180
2x + 2y = 120
x + y = 60

I don't know if this helps at all.

Remember, angles A and C are bisected, so the two adjacent angles are equal to each other (x, x and y, y)

Thanks for any help, BG

Join , and note that it is the bisector of , since the angle bisectors of a triangle are concurrent.



Also (exterior angle of )



is a cyclic quadrilateral (exterior angle = interior opposite angle)

Now join , and use angles in the same segment:

and



(isosceles )

Grandad