2.2 Definitions and Biconditional Statements

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# 2.2 Definitions and Biconditional Statements - PowerPoint PPT Presentation

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

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.
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

Biconditional Statement
• 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.
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.

• 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.

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.