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Proofs. 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.

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Presentation on theme: "Proofs. 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."— Presentation transcript:

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


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