Honors Geometry

1
Honors Geometry

• Lesson 2.4
• Conditional Statements

2
What You Should Learn Why You Should Learn It

• Goal 1 How to recognize and use conditional
  statements
• Goal 2 How to recognize and use postulates that
  are stated as conditional statements
• Reasoning correctly using conditional statements
  is a basic skill you need to argue convincingly
  in geometry, in law, and in advertising

3
Using Conditional Statements

• Conditional statement or an if-then statement
• If you study at least three hours, then you will
  pass the test
• A conditional statement has two parts
• The hypothesis, denoted by p
• The conclusion, denoted by q.
• In symbols, the statement if p, then q, is
  written a as

4
Using Conditional Statements

• The converse of the conditional statement is
  formed by interchanging the hypothesis and
  conclusion
• The converse of
• A conditional statement may be true or false, and
  its converse may be true or false

5
Using Conditional Statements

• To prove that a conditional statement is true,
  you must present an argument that the conclusion
  follows for all cases that fulfill the hypothesis
  
• To demonstrate that a conditional statement is
  false, you need describe only one example (called
  a counterexample) in which the hypothesis is
  fulfilled and the conclusion is not fulfilled

6
Conditional Statements and Converses (Example 1)

• Decide whether the statement and its converse are
  true

7
Conditional Statements and Converses Solution
(Example 1)

• a. The statement is true because 30 lt 90, but
  the conversesome acute angles do not measure
  30
• b. Both the statement and the converse are true
• c. The statement is false (some obtuse angles
  have measures that are not 120), but the
  converse is true

8
Biconditional Statement

• p if and only if q,
• This statement is equivalent to writing the
  conditional statement
• Example An angle is a right angle if and only
  if it measures 90
• A definition is always considered to be
  biconditional
• A right angle is an angle that measures 90

9
Translating Conditional Statements

• Translate to if-then form
• a. The defendant was in Dallas only on Saturdays
• b. Court begins only if it is 10 A.M.

10
Translating Conditional Statements Solution

• a. If the defendant was in Dallas, then it was a
  Saturday.
• b. If court begins, then it is 1000 a.m.

11
Using Postulates

• Postulates are assumed to be true
• They form the foundation on which other
  statements (called theorems) are built

12
Using Postulates
Postulate 7
13
The End