1. Proofs

2. Warm Up
Using the diagram below, create a problem to give to your partner
For example, what kind of angles are “blah” and “blah”
Or, if m<4 is “this”, what is the measure of blah blah

3. Review of Prior Knowledge
Triangle Angle Sum Theorem
Triangle Congruence Theorems
SAS, SSS, ASA
CPCTC
Congruence vs Equality
Properties of Congruence
Properties of Equality
Midpoints, Bisectors, Perpendicular

4. Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180º

5. Triangle Congruence Theorems

6. CPCTC “Corresponding Parts of Congruent Triangles are Congruent”
In other words, if you know two triangles are congruent, all the corresponding (matching) parts are also congruent

7. Congruence vs Equality
Remember, Angles and Lines Segments are things. We say that are congruent if they are the same.
Like your desks
The measures of angles and the lengths of segments are called equal if they are the same.
Like the dimensions or weight of your desks

8. Properties of Congruence

9. Properties of Equality
Addition: If a = b, then a + c = b + c
Subtraction: If a = b, then a – c = b – c
Multiplication: If a = b, then a * c = b * c
Division: If a = b and c ≠ 0, then a/c = b/c
Reflexive: a = a
Symmetric: If a = b, then b = a
Transitive: If a = b and b = c, then a = c
Substitution: If a = b, then b can replace a in any expression

10. Midpoints, Bisectors and Perpendicular
Midpoint: A point on a line segment that divides it into two equal parts.
Bisect: To cut in half
Perpendicular: Intersect at a right angle (90º)

11. PROOFS! Today and Friday we are going to prove the following theorems:
Vertical angles are congruent
Alternate Interior Angles
Points on a perp. Bisector are equidistant
In a parallelogram…
Opposite sides are congruent
Opposite angles are congruent
Diagonals bisect
Rectangles are parallelograms with congruent diagonals