JRLeon Discovering Geometry Chapter 4.8 HGSH C H A P T E R 4.8 O B J E C T I V E S  Discover properties of the base angles and the vertex angle bisector in isosceles triangles In this lesson you will ● Make a conjecture about the bisector of the vertex angle in an isosceles triangle ● Make and prove a conjecture about equilateral triangles ● Learn about biconditional conjectures A biconditional conjecture is a conjecture in which one condition cannot be true unless the other is also true. In other words, both the statement and its converse are true.

JRLeon Discovering Geometry Chapter 4.8 HGSH D D

We need to show that if AB  AC  BC, then  ABC is equiangular. 2. AB = BC GIVEN 1. AB = AC GIVEN 5. m  A = m  B = m  C Law of transitivity 4. m  A = m  C Isosceles Triangle Conjecture 3. m  B = m  C Isosceles Triangle Conjecture Flow Chart Proof: The Equilateral Triangle conjecture The converse of the Equilateral Triangle Conjecture is called the Equiangular Triangle Conjecture, and it states: If a triangle is equiangular, then it is equilateral. Is this true? Yes, and the proof is almost identical to the proof above, except that you use the converse of the Isosceles Triangle Conjecture. So, if the Equilateral Triangle Conjecture and the Equiangular Triangle Conjecture are both true, then we can combine them. Complete the conjecture below and add it to your conjecture list.

JRLeon Discovering Geometry Chapter 4.8 HGSH HOMEWORK: Lesson 4.8: Pages 245 – 246, Problems 1 through 6, 12