Mathematics Homework Help

1. a) Prove that the Isosceles Triangle Theorem (ITT) is true on the plane using SAS.

b) Prove that ITT is true on the plane using reflection in the angle bisector line.

c) Prove that ITT is true on the plane using reflection of the triangle across an arbitrary line followed by a translation

.2. Google the term “corollary” and write down the meaning that you found.

3. Prove the following corollary of ITT: The angle bisector of the angle between the two congruent sides of an Isosceles triangle is also a perpendicular bisector of the side opposite the bisected angle.

[Note: there are two things to prove here – that the angle bisector bisects the opposite side and it does so at a right angle].

4. a. Prove ITT is true for all triangles on the sphere. Which of the three proofs from the plane that you want to adapt is up to you, but you need only one proof.5a) State the converse* of ITT on the plane.

b) Prove the converse of ITT on the plane.

* note: The converse switches the order of the If portion and the Then portion of a proposition. For example, consider the following proposition: If I am a doctor Then I went to school for a long time. The converse to this proposition is: If I went to school for a long time Then I am a doctor. It is important to realize that sometimes the converse to a proposition is true and sometimes it is not true.