Conditional Statements and Geometric Proofs

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.

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

• 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.

What is the conclusion of the following statement: "The angles are supplementary, if they add up to 180 degrees."

• if they add up to 180 degrees
• the angles are supplementary
• they add up to 180 degrees
• there is no conclusion

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 this?

• Conditional Statement
• Inverse
• Converse
• THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

If it is a triangle then it has three sides.
What is the conclusion?

• it is a triangle
• it is a polygon
• it has three sides
• the polygon is a triangle

If it does not have four sides then it is not a rectangle.
What is the converse?

• If it is not a rectangle then it then it does not have  four sides.
• If it has four sides then it is a rectangle.
• If it is a rectangle then it has four sides.
• If it is not a rectangle then it has four sides.

p→q
What is the inverse?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

What does  
~q -> ~p symbolize?

• Conditional Statement
• Converse
• Inverse
• Contrapositive

Is the given statement true:
If the chair is empty, then class is not in session.

• True.  Class can't happen if a chair isn't occupied.
• False.  Someone could be absent.
• True. Nobody sits down so we don't do work.
• True.  There are no chairs here, so the hypothesis is true.