CONDITIONAL STATEMENTS

1
CONDITIONAL STATEMENTS

• REASONING CORRECTLY USING CONDITIONAL STATEMENTS
  IS A BASIC SKILL NEEDED TO ARGUE CONVINCINGLY IN
  GEOMETRY, IN LAW, AND IN ADVERTISING

2
UNDERSTANDING CONDITIONAL STATEMENTS

• ALSO KNOWN AS IF-THEN STATEMEMTS
• THERE ARE 2 PARTS, HYPOTHESIS, DENOTED BY p, AND
  THE CONCLUSION, DENOTED BY q. IF p THEN q.
• IN SYMBOLS p gt q.

3
CONVERSE STATEMENTS

• FORMED BY SWITCHING THE HYPOTHESIS AND CONCLUSION
• THE CONVERSE OF p q IS q p
• A CONDITIONAL STATEMENT MAY BE TRUE OR FALSE, AND
  ITS CONVERSE MAY BE TRUE OR FALSE.

4
PRACTICE

• Decide whether the statement and its converse are
  true.
• 1. If m lt P 900, then lt P is a right angle.
• 2. If m lt Q 1500, then lt Q is an obtuse angle.
• 3. If C lies interior of ltAOP, then
  mltAOC m ltCOP mltAOP.
• 4. If C lies between A and Z, then
  AC CZ AZ.

5
BICONDITIONAL STATEMENT

• IF AND ONLY IF
• p ? q
• INCLUDES BOTH THE CONDITIONAL p q AND ITS
  CONVERSE q p
• A DEFNITION IS CONSIDERED A BICONDITIONAL
  STATEMENT

6
POINT, LINE, AND PLANE POSTULATES

• POSTULATE 5 THROUGH ANY 2 DISTINCT POINTS THERE
  EXISTS EXACTLY ONE LINE
• 6 A LINE CONTAINS AT LEAST 2 POINTS
• 7 THROUGH ANY 3 NONCOLLINEAR POINTS THERE EXISTS
  EXACTLY 1 PLANE

7
POINT, LINE, AND PLANE POSTULATES

• 8 A PLANE CONTAINS AT LEAST 3 NONCOLLINEAR
  POINTS
• 9 IF 2 DISTINCT POINTS LIE IN A PLANE, THEN THE
  LINE CONTAINING THEM LIES IN THE PLANE
• 10 IF 2 DISTINCT PLANES INTERSECT, THEN THEIR
  INTERSECTION IS A LINE.