Lesson 2.1 AIM: Conditional Statements

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Presentation transcript:

Lesson 2.1 AIM: Conditional Statements DO NOW: Find a counterexample. The sum of two numbers is always greater than either of the two numbers being added. -2 + -3 = -5

A conditional statement is composed of a hypothesis and a conclusion.

Write as a conditional statement. A rectangle has four right angles. If a shape is a rectangle, then it has four right angles.

Finding a Counterexample. If it is February, then there are only 28 days in the month. Every leap year, the month of February has 29 days.

Writing the Converse. To write the Converse, switch the hypothesis and the conclusion. If two lines intersect to form right angles, then they are perpendicular. If two lines are perpendicular, then they form right angles.

Which conditional has a false converse? If two planes are parallel, then they have no points in common. Converse: If two planes have no points in common, then the planes are parallel. If a figure is a square, then it has four sides. Converse: If a figure has four sides, then it is a square. If a point has x-coordinate 0, then it lies on the y-axis. Converse: If a point lies on the y-axis, then the point has an x-coordinate 0. If two angles are congruent, then they have the same measure. Converse: If two angles have the same measure, then they are congruent.

Which conditional has a false converse? If two planes are parallel, then they have no points in common. Converse: If two planes have no points in common, then the planes are parallel. If a figure is a square, then it has four sides. Converse: If a figure has four sides, then it is a square. This converse is false. If a point has x-coordinate 0, then it lies on the y-axis. Converse: If a point lies on the y-axis, then the point has an x-coordinate 0. If two angles are congruent, then they have the same measure. Converse: If two angles have the same measure, then they are congruent.

Summary Question Fill in the blanks. 1. A conditional statement has two parts: a ____________ and a ______________. 2. To find the converse of a conditional you __________ the hypothesis and conclusion.