# Chapter 4: Discovering and Proving Triangle Properties

Mind Map by Ashley Phillips , updated more than 1 year ago
 Created by Ashley Phillips about 5 years ago
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### Description

Mind Map on Chapter 4: Discovering and Proving Triangle Properties, created by Ashley Phillips on 11/04/2015.

## Resource summary

Chapter 4: Discovering and Proving Triangle Properties
1 4.1 Triangle Sum Conjecture
1.1 The sum of the measures of the angles in every triangle is 180 degrees.
2 4.2 Properties of Isosceles triangles
2.1 Vertex angle: The angle between the two congruent sides The base angles are the other two angles. The side between the two base angle is called the base. The other two sides are caused legs.
3 4.3 Triangle Inequality conjecture
3.1 The sum of the lengths of any two sides of a triangle is more than the length of the third side.
3.2
4 4.4 and 4.5 Are there congruent shortcuts?
4.1 SSS
4.1.1 SAS
4.1.1.1 ASA
4.1.1.1.1 SAA
4.1.1.1.1.1 SSA
4.1.1.1.1.1.1 AAA
4.1.1.1.1.1.1.1 Three pairs of congruent angles
4.1.1.1.1.1.1.1.1 Works
4.1.1.1.1.1.2 Two pair of congruent sides and one pair of congruent angles.
4.1.1.1.1.1.2.1 Doesn't work
4.1.1.1.1.2 Two pair of congruent angles and one pair of congruent sides(nots not between the pair of angles)
4.1.1.1.1.2.1 Works
4.1.1.1.2 Two pair pair of congruent angle and one pair of congruent sides(sides between the pair of angles)
4.1.1.1.2.1 Works
4.1.1.2 Two pairs of congruent sides and one pair of congruent angles.(angles between the pair of sides.
4.1.1.2.1 Works
4.1.2 Three pairs of congruent sides
4.1.2.1 Works
4.2 4.6 Corresponding Parts of Congruent triangles
4.2.1 If you use a congruence shortcut, then you can use CPCTC to show that any of their corresponding parts are congruent
4.2.2 4.7 Flowchart thinking
4.2.2.1 Flowchart proofs are when you fill in boxes for a proof instead of a two column proof.
4.2.2.2 4.8 Proving Special Triangle Conjectures
4.2.2.2.1 Vertex angleBisector Conjecture
4.2.2.2.1.1 In an isosceles triangle the bisector of the vertex angle is also equiangular and equilateral.
4.3

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