Biconditional

Write a definition of congruent angles as a biconditional statement.

• Angles are congruent if they have the same size and shape.

• If angles are congruent, then they have the same size and shape.

• Congruent angles are the same.

• Angles are congruent if and only if they have the same size and shape.

Tags

CCSS.8.G.A.2

Write a definition of a right angle as a biconditional statement.

• An angle is a right angle if and only if it has a measure of 90 degrees.

• An angle has a measure of 90 degrees if and only if it is a right angle.

• Right angles are 90 degrees.

• If an angle is a right angle, then it has a measure of 90 degrees.

Tags

CCSS.4.G.A.1

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.

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

Points lie in one plane if and only if they are coplanar.

• Coplanar points lie in one plane.

• If points lie in one plane, then they are coplanar.

• If points are coplanar, then they lie in one plane.

• Planes have coplanar points.

Write the conditional statements as a biconditional statement:

1) If B is between A and C, then AB+BC=AC.

2) If AB+BC=AC, then B is between A and C.

• Segment Addition Postulate

• B is between A and C when AB+BC=AC if and only if Segment Addition Postulate.

• B is between A and C if and only if AB+BC=AC.

Select the counterexample to the conditional statement:

If  $n^{2\ }=\ 5n$  , then  $n=5$ .

•  $n=-5$  

•  $n=0$  

•  $n=5$  

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Identify the hypothesis and conclusion:

If  $3x-7=32$  , then  $x=13.$ 

• Hypothesis:  $3x-7=32$  
  Conclusion: $x=13$  

• Hypothesis: $x=13$  
  Conclusion:  $3x-7=32$  

Tags

CCSS.HSA.REI.A.1

A biconditional statement..

• is an "if/then" statement

• uses the phrase "if and only if"

• is the first part of a statement

• is the second part of a statement

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 is the biconditional that matches the statement below: An even number is a number that is divisible by 2.

• A number is even if and only if it is divisible by 2.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.