2.2 Definitions and Biconditional Statements

1. 2.2 Definitions and Biconditional Statements Geometry

2. Goals • Recognize and use definitions • Recognize and use biconditional statements Geometry

3. Perpendicular Lines • 2 lines that intersect to form a right angle • Line Perpendicular to a Plane • A line that intersects a plane in a point and is perpendicular to every line in the plane that it intersects • The symbol  is read as “is perpendicular to” n m m ┴ n Geometry

4. Example 1: Using Definitions • Decide whether each statement about the diagram is true. Explain your answer. • Points D, X, and B are collinear. • Line AC is ┴ to line DB • Angle AXB is adjacent to angle CXD True True A False X D B C Geometry

5. Using Biconditional Statements • Conditional statements can also be written only-if form • It is Saturday, only if I am working at the store • Hypothesis- it is Saturday • Conclusion- I am working at the store • Biconditional Statement • Is a statement that contains the phrase “if and only if” • This is equivalent to writing a conditional statement and its converse Geometry

6. Example 2: Writing a Postulate as a Biconditional • The converse of the Angle Addition Postulate is true. Write the converse and combine it with the postulate to form a true biconditional statement. • Converse • If m<RSP + m<PST = m<RST, then P is on the interior of <RST. • Biconditional • P is in the interior of <RST if and only if m<RSP + m<PST = m<RST Geometry