If a conditional statement is \(p\rightarrow q\), then the inverse is \(\sim p\rightarrow \sim q\).Ī statement is logically equivalent if the "if-then" statement and the contrapositive statement are both true.Ī premise is a starting statement that you use to make logical conclusions. Note that the converse of a statement is not true just because the original statement is true. If a conditional statement is \(p\rightarrow q\) (if \(p\), then \(q\)), then the converse is \(q\rightarrow p\) (if \(q\), then \(p\). If a conditional statement is \(p\rightarrow q\) (if \(p\) then q), then the contrapositive is \(\sim q\rightarrow \sim p\) (if not q then not p). What if you were given a conditional statement like "If I walk to school, then I will be late"? How could you rearrange and/or negate this statement to form new conditional statements?Ī statement is biconditional if the original conditional statement and the converse statement are both true.Ī conditional statement (or 'if-then' statement) is a statement with a hypothesis followed by a conclusion. three points on a triangle are collinear if and only if they satisfy certain criteria) is also true and is extremely powerful in proving that three points are collinear. In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. In other words, if \(p\rightarrow q\) is true and \(q\rightarrow p\) is true, then \(p \leftrightarrow q\) (said “\(p\) if and only if \(q\)”). Menelaus' theorem relates ratios obtained by a line cutting the sides of a triangle. The sum of the areas of the two squares on the legs ( a and b) equals the area of the square on the hypotenuse ( c ). When the original statement and converse are both true then the statement is a biconditional statement. The converse and inverse may or may not be true. Compare AED with CEF: E is the midpoint of AC (Given) 2. In ABC, through C, draw a line parallel to BA, and extend DE such that it meets this at F, as shown below: Mid Point Theorem Proof. ![]() Then click Next Question to answer the next Pre-AP Geometry. The contrapositive is logically equivalent to the original statement. D and E are the mid-points of sides AB and AC of ABC respectively. Note to student: This packet should be used as practice for the Geometry 22 final exam. If the “if-then” statement is true, then the contrapositive is also true.
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