Conditional, Converse, and Bi Conditional Statements

2.1 Conditional and Converse Statements

Multiple Choice

When taking the converse we ___________ the hypothesis and conclusion.

• don't change

• switch

• highlight

• delete

Multiple Choice

Is the Conditional Statement True or False: If a shape is a square, then it has four sides.

• False

• True, all squares have four sides

Multiple Choice

Converse: If a shape has four sides, then it is a square.

• False, it could be any quadrilateral and have four sides

• True

Open Ended

Write the converse of the following conditional statement: If two angles have the same measure, then they are congruent.

Multiple Choice

Which is the converse of the statement?

• If you are not a guitar player, then you are not a musician.

• If you are a musician, then you are a guitar player.

• If you are a guitar player, then you are not a musician.

• If you are not a musician, then you are not a guitar player.

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.
• "If angles are not congruent, then the measures of the angles are not equal."
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Biconditional Statements

Example 1

Conditional: If two lines are perpendicular, then they form a right angle.

Converse: If two lines form a right angle, then they are perpendicular.

Both the conditional and converse are true, so this is biconditional.

Example 1 Continued

Now we can write the statement in the "if and only if" form.

Biconditional: Two lines are perpendicular if and only if they form a right angle.

*Notice how the words "if" and "then" were removed and the hypothesis and conclusion were connected with the phrase "if and only if" in the middle.

Multiple Choice

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

• conditional has to be true
• converse of the conditional has to be true
• all the above

Multiple Choice

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.

Multiple Select

Select the conditional statement of the biconditional statement:

I am a junior if and only if I am in 11th grade.

• I am a junior

• If I am a junior, then I am in 11th grade.

• I am in 11th grade

Multiple Choice

Is this a true biconditional statement? "If a shape is a triangle, then it has 3 sides."

• Yes

• No

Multiple Choice

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.

Multiple Choice

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

• "If angles are not congruent, then the measures of the angles are not equal."

Multiple Choice

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• If a polygon is a trapezoid, then it is a quadrilateral.

• A rectangle is also a quadrilateral.

Open Ended

Write a converse statement for the conditional statement below:

If the triangle is isosceles, then it's an equilateral.

Open Ended

Is the statement: 'If two angles have the same measure, then they are congruent' biconditional? If yes, write it in the form with 'if and only if'.

Multiple Select

Which of the following conditional statements and their converses can be written as a biconditional statement?

• If a polygon has 4 sides, then it is a quadrilateral.

• If you play guitar, then you are a musician.

• If the diagonals are perpendicular, then it’s a quadrilateral with adjacent congruent sides.

• If a quadrilateral with opposite sides are parallel, then it is a parallelogram.