Biconditional Statements

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.HSG.CO.A.1

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.HSG.C.A.2

CCSS.HSG.CO.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

Determine if the statement is true or false. Then write the converse.

If Jake lives in Ramsey, then he lives in New Jersey

• True; If Jake lives in Ramsey, then he lives in New Jersey.

• True; If Jake lives in New Jersey, then he lives in Ramsey.

• False; If Jake lives in Ramsey, then he lives in New Jersey.

• False; If Jake lives in New Jersey, then he lives in Ramsey.

Describe the validity of the conditional statement?

If Jake lives in New Jersey, then he lives in Ramsey.

• Always True

• Sometimes True

• Never True

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6