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2.2 Definitions and Biconditional Statements

2.2 Definitions and Biconditional Statements. 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.

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2.2 Definitions and Biconditional Statements

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  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. • Points D, X, and B are collinear. • AC is perpendicular to DB. • <AXB is adjacent to <CXD. . A . . D X B . C

  4. Biconditional Statement • Biconditional Statement • It is Saturday, only ifI 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 x2 = 9. • Is this a biconditional statement? Yes • 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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