2.2 Biconditional Statements

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

• if

• then

• if and only if

• always

What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."

• If an angle has 90 degrees, then it is a right angle.
• If an angle is a right angle, then it has 90 degrees.
• An angle is a right angle if and only if it has 90 degrees.

Tags

CCSS.HSG.CO.A.1

  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.

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

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 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.

Can a true biconditional statement be written from the conditional "If a shape is a triangle, then it has 3 sides."

• Yes

• No

Tags

CCSS.HSG.CO.A.1

What counterexample makes the following biconditional false?

"It is Halloween if and only if it is October 31."

• This is a true biconditional, so it has no counterexamples.

• It is not October 31.

• I don't celebrate Halloween.

• It is October 30.

Determine the truth value of the given statement.

" If a number is odd, then it is divisible by 2."

• True

• False

Determine if the conditional statement is true or false.

If two angles are vertical, then they are congruent.

• True

• False