2.3 Biconditionals

Presentation

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Mathematics

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10th Grade

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Practice Problem

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Medium

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CCSS

L.2.1F, 7.G.A.2, 2.MD.A.3

Standards-aligned

Kimberly Brightmore

Used 43+ times

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6 Slides • 10 Questions

2.3 Biconditionals

Geometry CP

Biconditional Review

A statement that contains the phrase "if and only if."
"if and only if" is abbreviated using iff

To determine if a statement is a true biconditional, both the conditional and converse must be true!

Conditional: If the shape has 3 sides, then it is a triangle.
Converse: If it is a triangle, then the shape has 3 sides.
Conditional is TRUE, Converse is TRUE, so Biconditional is TRUE.

To determine if a statement is a true biconditional, both the conditional and converse must be true!

Conditional: If it is a square, then the shape has 4 sides.
Converse: If the shape has 4 sides, then it is a square.
Conditional is TRUE, Converse is FALSE, so Biconditional is FALSE.

Multiple Choice

What is the conditional statement from the following biconditional:

Two angles are supplementary if and only if the sum of their measures is 180°.

If the sum of their measures is 180º, then two angles are supplementary.

If two angles are supplementary, then the sum of their measures is 180º.

Multiple Choice

What is the converse statement from the following biconditional:

Two angles are supplementary if and only if the sum of their measures is 180°.

If the sum of their measures is 180º, then two angles are supplementary.

If two angles are supplementary, then the sum of their measures is 180º.

Multiple Choice

What is the conditional statement from the following biconditional:

Three points are collinear iff all three points lie on the same line.

If three points are collinear, then all three points lie on the same line.

If all three points lie on the same line, then three points are collinear.

Multiple Choice

What is the converse statement from the following biconditional:

Three points are collinear iff all three points lie on the same line.

If three points are collinear, then all three points lie on the same line.

If all three points lie on the same line, then three points are collinear.

Fill in the Blanks

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Fill in the Blanks

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How to write a conditional as a biconditional

If two segments are the same size, then they are congruent.
Cross out the IF and the THEN.
Rewrite the statement using IFF in the spot where the "then" used to be.
Two segments are the same size iff they are congruent.

Fill in the Blanks

Type answer...

Fill in the Blanks

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TRUE vs. FALSE Biconditionals

If ...
the conditional statement is true
the converse statement is true
then the biconditional is true.

Multiple Choice

Is the biconditional true or false?

Biconditional: It is Saturday iff I do not have school.

Conditional: If it is Saturday, then I do not have school.

Converse: If I do not have school, then it is Saturday.

True

False

Multiple Choice

Is the biconditional true or false?

Biconditional: Three points are coplanar if and only if they lie in the same plane.

Conditional: If three points are coplanar, then they lie in the same plane.

Converse: If they lie in the same plane, the three points are coplanar.

True

False

2.3 Biconditionals

Geometry CP

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