Can a transversal intersect one side of a triangle internally and the other two sides externally?

Can a transversal intersect one side of a triangle internally and the other two sides externally? Ans: No. Solution: Pasch’s axiom says that if a line intersects one side of a triangle (internally), then it must intersect another side of the triangle (internally).

How do you prove the exterior angle bisector theorem?

Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

1. Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC produced in D.
2. Prove that : BD / CD = AB / AC.

What is internal and external bisector of an angle?

The internal (external) bisector of an angle of a triangle divides the opposite side internally (externally) in the ratio of the corresponding sides containing the angle.

Under what conditions would the Orthocenter of a triangle lie outside the triangle?

Under what conditions would the orthocenter of a triangle lie outside the triangle? Solution: Any obtuse triangle. The altitudes drawn to the sides of the obtuse angle always lie outside the triangle.

How do you use the Menelaus Theorem?

For plane geometry, the Theorem of Menelaus is — given any line that transverses (crosses) the three sides of a triangle (one of them will have to be extended), six segments are cut off on the sides. The product of three non-adjacent segments is equal to the product of the other three. The converse also holds.

What is external bisector theorem?

External Angle Bisector Theorem The external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

What is internal angle bisector theorem?

Interior Angle Bisector Theorem : The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle. Given : A ΔABC in which AD is the internal bisector of ∠A and meets BC in D. Prove that : BD / DC = AB / AC.

What is the meaning of external bisector?

The external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

What is internal angle bisector?

The (interior) bisector of an angle, also called the internal angle bisector (Kimberling 1998, pp. 11-12), is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter. , which has trilinear coordinates 1:1:1.