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 they 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