Biconditionals & Definitions (Day 2)

Write the true biconditional for the statement:  $If\ x\ =\ 12,\ then\ 2x\ -\ 5\ =\ 19.\$  

•  $If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.\$  

•  $x\ =\ 12\ if\ and\ only\ if\ 2x\ -\ 5\ =\ 19.\$  

•  $x\ =\ 12\ and\ 2x\ -\ 5\ =\ 19.\$  

• This statement cannot be written as a true biconditional. 

Test the statement below to see if it is reversible. If so, write it as a biconditional.

Complementary angles are two angles with measures that have a sum of 90.

• Reversible; If two angles are complementary, then the sum of their measures is 90.

• Reversible; Two angles are complementary if and only if the sum of their measures is 90.

• Not reversible.

When can a biconditional statement be true?

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.

What phrase does a biconditional statement use?

• if, then
• if, when
• if and only if
• then, if

What has to happen in order to write a biconditional statement?

• conditional has to be true

• converse of the conditional has to be true

• both of these

• none of these

  Rewrite the following statement as a      biconditional: "Supplementary angles add up to 180"

• If two angles add up to 180^o then they are supplementary.
• You can't it is conditional.
• Two angles are supplementary if and only if the sum of the measure of the two angles is 180^o.
• If two angles sum does not equal 180^o then they are not supplementary.

What is a converse of a conditional?

• take out the hypothesis
• take out the conclusion
• switch the hypothesis and conclusion
• make it false

Which two statements  make, "A polygon is a triangle if and only if it has exactly 3 sides." biconditional. 

• 1. If a polygon is a triangle, then the polygon has exactly three sides. 2 If a polygon has exactly three sides then it is a triangle
•  1. If a polygon is not a triangle,  then the polygon does not have three side. 2.  If a polygon does not have three sides,then it is not a triangle.

Select the conditional statement(s) of the biconditional statement.

Points are collinear if and only if they all lie in one line.

• If collinear points lie in one line, then they are a line.

• If points all lie in one line, then they are collinear.

• Collinear points lie in one line.

• If points are collinear, then they all lie in one line.

Write the statement below as a conditional statement.

Vertical Angles are congruent

• Two angles are vertical if and only if they are congruent.

• If two angles are congruent, then they are Vertical.

• If two angles are Vertical, then they are congruent.