Warm Up 2-23.  In a conditional statement, the “if” portion of the statement is called the hypothesis, and the “then” portion is called the conclusion.  If you reverse the order of the hypothesis and conclusion, then you have created the converse of the statement. Write the converse of the conditional statement: If angles are vertical angles, then they are congruent. If angles are congruent, then they are vertical angles. Is the original statement true?  Is the converse true?  Justify your answer. Original is true but not converse because there are other congruent angles that are not vertical (ex: corresponding)

HW: 2-27 through 2-32 2.1.3  Converses October 1, 2018

Objectives CO: SWBAT write the converse relationship of conditional statements. LO: SWBAT investigate the relationship between the truth of a statement and the truth of its converse. 

Progress Chart a-b c-e Purple Stripes Blue Green Pink Orange Yellow Red

2-24. Every conditional statement has a converse 2-24. Every conditional statement has a converse.  Consider the arrow diagram for a familiar relationship below.  Triangles congruent → all pairs of corresponding sides are congruent. In mathematics, to say that a statement is true, it must always be true.  That is, it must follow from a definition or a theorem.  Is this arrow diagram true? Write the converse of this arrow diagram as an arrow diagram or as a conditional statement.  Is this converse true?  Justify your answer. All pairs of corresponding sides are congruent → triangles congruent Yes, because of SSS congruence Now consider another statement below.  Is this statement true? Triangles congruent  →  all pairs of corresponding angles are congruent. Write its converse.  Is the converse true?  If it is true, prove it.  If it is not always true, give a counterexample.  A counterexample is a statement showing at least one situation where a statement is false. All pairs of corresponding angles are congruent → triangles congruent No, because you can make a smaller triangle with the same angles Write the converse of the arrow diagram below.  Is this converse true?  Justify your answer. A polygon is a rectangle  →  the area of the polygon is b · h. The area of the polygon is b · h → the polygon is a rectangle No, because parallelograms also have the area b · h If true, true, then DEFINITION Progress Chart

Hot potato All squares are rhombuses. 2-25.  For each statement below, rewrite it as a conditional statement or as an arrow diagram, and state whether it is true or false.  Then write the converse of the statement and tell whether it is true or false.  Remember that for a mathematical statement to be true, it must always be true.  Justify your answers. All squares are rhombuses. If a figure is a square, then it is a rhombus. If a figure is a rhombus, then it is a square. Every isosceles triangle is equilateral. If a triangle is isosceles, then it is equilateral. If a triangle is equilateral, then it is isosceles. Two parallel lines cut by a transversal form same-side interior angles that are supplementary If two parallel lines are cut by a transversal, then same-side interior angles are supplementary. If same-side interior angles are supplementary, then the two lines cut by the transversal must be parallel Hot potato