2-2 B ICONDITIONALS & D EFINITIONS M11.B.2 O BJECTIVES : 1) T O WRITE BICONDITIONALS 2) T O RECOGNIZE GOOD DEFINITIONS.

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Presentation transcript:

2-2 B ICONDITIONALS & D EFINITIONS M11.B.2 O BJECTIVES : 1) T O WRITE BICONDITIONALS 2) T O RECOGNIZE GOOD DEFINITIONS

V OCABULARY When a conditional and its converse are true, you can combine them as a true biconditional. **You write a biconditional by joining the two parts of each conditional with the phrase if and only if.

E XAMPLE : C ONSIDER THIS TRUE C ONDITIONAL S TATEMENT Write its converse. If the converse is also true, combine the statements as a biconditional. Conditional: If x = 5, then x + 15 = 20 Converse: Biconditional:

E XAMPLE Consider this true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. Conditional: If three points are collinear, then they lie on the same line. Converse: Biconditional:

E XAMPLE : S EPARATING A B ICONDITIONAL I NTO P ARTS Write the two statements that form this biconditional. Lines are skew if and only if they are noncoplanar.

U SING S YMBOLS COPY THE ORANGE BOX ON PAGE 76 INTO YOUR NOTEBOOKS!

G OOD D EFINITIONS **A good definition is a statement that can help you identify or classify an object. 1) Use clearly understood terms. The terms should be commonly understood or already defined. 2) Are precise. Avoid words such as: large, sort of, and some. 3) Are reversible. You can write it as a true biconditional. One way to show that a statement is NOT a good definition is to find a counterexample.

E XAMPLE Definition: A right angle is an angle whose measure is 90. Conditional: Converse: Biconditional

E XAMPLE Is the following statement a good definition? Explain. ** A square is a figure with four right angles. ** A triangle has sharp corners.