1. Proofs Geometry - Chapter 2

2. Proof Step – by – step from given to answer Each step has a reason
Reasons are theorems, postulates or definitions
Two types:
Algebraic – Solving mathematical equations
Geometric – Proving or finding measures

3. Algebraic Proof Tools (Reasons)

4. Algebraic Proof Tools (Reasons)

5. Example
Algebraic Example:
Solve: -5 = 3n + 1
Solve for x:

6. Geometric Proofs Geometry 2.6
Typically used to establish relationships or prove congruence
Then used to solve or work with Algebraic aspects
Definitions – Statements that describe a mathematical object or relationship
Postulates – Relationships that have always proven accurate (accepted without proof)
Theorems – Statements that have been proven

7. Geometric Proofs - Example Geometry 2.6

8. Triangles
Attributes: What do we know about triangles?

9. Triangles Types - Classifications By Angles: By Congruent Parts: Acute
Obtuse
Right
By Congruent Parts:
Scalene
Isosceles
Equilateral

10. Triangles – Angle Relationships Geometry 4.3
Triangle Sum Theorem
Sum of the angle measures of a triangle is 180o
Example: p. 232
Exterior Angle Theorem
Measure of the exterior angle of a triangle = sum of the opposite interior angles
Example: p. 233
Third Angle Theorem
If 2 angles of one triangle are congruent to 2 angles of another – their third angles are congruent
Example: p. 234

11. Congruence - Congruent Figures Geometry 4.4
Same Size – Same Shape
All angles are congruent (same measure)
All lengths are congruent (same length)
Any shape, 2 or 3 dimensional
Labeling:
Congruent parts in the same order in both figures

12. Triangle Congruence (4.5-4.7)
Several ways to prove congruence
SSS – Three sides congruent: p. 250
SAS – Two sides & included angle: p. 251
ASA – Two angles & included side: p. 261
AAS – Two angles and an adjoining side: p. 262
HL (Right Triangles only) – Hypotenuse/Leg: p. 263
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
P. 268

13. Parallelograms Attributes - Quadrilateral Special Cases
Both pairs of opposite sides are Parallel
Both pairs of opposite sides are congruent
One pair opposite sides are congruent AND parallel
Diagonals of quadrilateral bisect each other
Both pairs of opposite angles are congruent
Special Cases
Rectangle
Rhombus
Square

14. Parallelograms Using Attributes in Proofs To prove a parallelogram
To prove triangles