What Are the Proofs for Triangle Properties in Euclidean Geometry?

[k3N70n]

Euclidean Geometry

Homework Statement

I'm not looking for any answer, I'm just having a hard time understanding what these two questions are asking for:

1. Prove that the external bisector of an angle of a triangle (not isosceles) divides the opposite side (externally) into two segments proportional to the sides of the triangle adjacent to the angle.


2. Prove that two vertices of a triangle and the feet of the altitudes to the sides adjacent to the third vertex can be inscribed in a circle. (The feet are the points of intersection of the altitude with the opposite sides of the triangle).

If someone would help me with a picture or something that would be ideal. Thank you kindly,
Kenton.

 

[Hurkyl]

1. Prove that the external bisector of an angle of a triangle (not isosceles) divides the opposite side (externally) into two segments proportional to the sides of the triangle adjacent to the angle.


Draw a triangle ABC.

Extend the line segment AB through A. Let D be a point on that extension.

CAD is an external angle at A, is it not?

Draw the angle bisector of CAD.

Extend side BC.

The line BC intersects the angle bisector of CAD, does it not?