CONDITIONAL STATEMENTS Section 2-1. Objectives  To recognize conditional statements.  To write converses of conditional statements.

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Presentation transcript:

CONDITIONAL STATEMENTS Section 2-1

Objectives  To recognize conditional statements.  To write converses of conditional statements.

Have you ever heard a person say: If you are not completely satisfied, then your money will be refunded? This is an if-then statement called a ______________.

Every conditional statement has two parts. The part following the if is the _____________. The part following the then is the ___________.

Example 1:Identify the Hypothesis and the Conclusion If today is the first day of fall, then the month is September. Hypothesis: Conclusion:

Example 2:Identify the Hypothesis and the Conclusion If you want to be fit, then get plenty of exercise. Hypothesis: Conclusion:

Converse To find the Converse of a Conditional -Switch the Hypothesis and Conclusions around, But you keep the “IF” and “Then” where they are.

Write the converse of the conditional statement. Example : If two lines are not parallel and do not intersect, then they are skew lines.

Write the converse of the conditional statement Example : If you eat your vegetables, then you grow.

Write the converse of the conditional statement Example: If a triangle is a right triangle, then it has a 90 degree angle.

Truth Values (true or false?) Converses are NOT ALWAYS TRUE. Write the converse of the conditional AND determine it’s truth value. If a figure is a square, then it has four sides.

Truth Values (true or false?) Example: Write the converse of the conditional AND determine it’s truth value. If two lines do not intersect, then they are parallel.

Truth Values (true or false?) Example: Write the converse of the conditional AND determine it’s truth value. If x = 2, then |x| = 2.

BICONDITIONALS AND DEFINITIONS Section 2-2

Objectives  To write biconditionals.  To recognize good definitions.

Objective A ______________ is the combination of a conditional statement and its converse. A biconditional (statement) contains the words “___________________.”

Consider the true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. 1. Conditional: If two angles have the same measure, then the angles are congruent.

Consider the true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. 2. Conditional: If three points are collinear, then they lie on the same line.

Recognizing a Good Definition - Use the examples to identify the figures above that are polyglobs. Write a definition of a polyglob by describing what a polyglob is. See Page 76

Show that the definition is reversible. Then write it as a true biconditional. 1. Definition: Perpendicular lines are two lines that intersect to form right angles.

Show that the definition is reversible. Then write it as a true biconditional. 2. Definition: A right angle is an angle whose measure is 90 (degrees).

Is the given statement a good definition? Explain. 1. An airplane is a vehicle that flies. 2. A triangle has sharp corners. 3. A square is a figure with four right angles.

DEDUCTIVE REASONING “LAWS OF DETACHMENT/SYLLOGISM” Section 2-3

Classwork Page – 26 even, 54 – 58 Page 78 1 – 12, 27 – 35, 41 – 43 Page 84 1 – 15 odd Page