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2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular.

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Presentation on theme: "2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular."— Presentation transcript:

1 2.2 Definitions and Biconditional Statements

2 Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular to a plane is a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.

3 Exercise Decide whether each statement about the diagram is true. Explain your answer using the definitions you have learned. a.Points D, X, and B are collinear. b.AC is perpendicular to DB. c.<AXB is adjacent to <CXD. A B C DX....

4 Biconditional Statement – It is Saturday, only if I am working at the restaurant. Conditional Statement – If it is Saturday, then I am working at the restaurant.

5 Consider the following statement x = 3 if and only if x 2 = 9. a.Is this a biconditional statement? Yes a.Is the statement true? No, because x also can be -3.

6 Rewrite the biconditional as conditional statement and its converse. – Two angles are supplementary if and only if the sum of their measures is 180°. – Conditional: If two angles are supplementary, then the sum of their measures is 180°. – Converse: If the sum of two angles measure 180°, then they are supplementary.

7 State a counterexample that demonstrates that the converse of the statement is false. – If three points are collinear, then they are coplanar. – If an angle measures 48°, then it is acute.

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