Conditional Statements and Related Conditional

Conditional Statement: If a triangle has 3 congruent sides, then it's an equilateral triangle.

Identify the converse of this conditional statement:

• If a triangle does not have 3 congruent sides, then it's not an equilateral triangle.

• If a triangle is equilateral, then it has 3 congruent sides.

• If a triangle is not equilateral, then it does not have 3 congruent sides.

• If a triangle has 3 congruent sides, then it's not an equilateral triangle.

Answer explanation

The converse of a conditional statement reverses the hypothesis and conclusion. Here, the original statement is 'If a triangle has 3 congruent sides, then it's an equilateral triangle.' The converse is 'If a triangle is equilateral, then it has 3 congruent sides.'

Conditional Statement: If a triangle has 3 congruent sides, then it's an equilateral triangle.

Identify the inverse of this conditional statement:

• If a triangle does not have 3 congruent sides, then it's not an equilateral triangle.

• If a triangle is equilateral, then it has 3 congruent sides.

• If a triangle is not equilateral, then it does not have 3 congruent sides.

• If a triangle has 3 congruent sides, then it's not an equilateral triangle.

Answer explanation

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q." Here, P is "a triangle has 3 congruent sides" and Q is "it's an equilateral triangle." Thus, the correct inverse is "If a triangle does not have 3 congruent sides, then it's not an equilateral triangle."

Write the converse, inverse, and contrapositive of each statement. (match)

If segments are congruent, then they have equal measures.

• inverse

• If segments do not have equal measures, then they are not congruent.

• contrapositive

• If segments are not congruent, then they do not have equal measures.

• converse

• If segments have equal measures, then they are congruent.

Conditional Statement: If a triangle has 3 congruent sides, then it's an equilateral triangle.

Identify the contrapositive of this conditional statement:

• If a triangle does not have 3 congruent sides, then it's not an equilateral triangle.

• If a triangle is equilateral, then it has 3 congruent sides.

• If a triangle is not equilateral, then it does not have 3 congruent sides.

• If a triangle has 3 congruent sides, then it's not an equilateral triangle.

Answer explanation

The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P." Here, "not Q" is "not an equilateral triangle" and "not P" is "does not have 3 congruent sides." Thus, the correct choice is: If a triangle is not equilateral, then it does not have 3 congruent sides.

Conditional Statement: If an angle measures 30 degrees, then it's an acute angle.

Identify the converse of this conditional statement:

• If an angle measures 30 degrees, then it's not an acute angle.

• If an angle does not measure 30 degrees, then it's not an acute angle.

• If an angle is not acute, then it does not measure 30 degrees.

• If an angle is acute, then it measures 30 degrees.

Answer explanation

The converse of a conditional statement "If P, then Q" is "If Q, then P." Here, the original statement is "If an angle measures 30 degrees (P), then it's an acute angle (Q)." Thus, the converse is "If an angle is acute (Q), then it measures 30 degrees (P)."

Conditional Statement: If an angle measures 30 degrees, then it's an acute angle.

Identify the inverse of this conditional statement:

• If an angle measures 30 degrees, then it's not an acute angle.

• If an angle does not measure 30 degrees, then it's not an acute angle.

• If an angle is not acute, then it does not measure 30 degrees.

• If an angle is acute, then it measures 30 degrees.

Answer explanation

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q." Here, P is "an angle measures 30 degrees" and Q is "it's an acute angle." Thus, the correct inverse is "If an angle does not measure 30 degrees, then it's not an acute angle."

Conditional Statement: If an angle measures 30 degrees, then it's an acute angle.

Identify the contrapositive of this conditional statement:

• If an angle measures 30 degrees, then it's not an acute angle.

• If an angle does not measure 30 degrees, then it's not an acute angle.

• If an angle is not acute, then it does not measure 30 degrees.

• If an angle is acute, then it measures 30 degrees.

Answer explanation

The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P." Here, "not Q" is "not acute" and "not P" is "not measuring 30 degrees." Thus, the correct contrapositive is: If an angle is not acute, then it does not measure 30 degrees.

Select the appropriate choice related to the truth value of the following conditional statement:

If an angle is acute, then it measures 30 degrees.

• True. All acute angles measure 30 degrees.

• False. An angle can be acute and not measure 30 degrees. Counterexample: An angle measuring 20 degrees is acute and does not measure 30 degrees.

• False. Some 30-degree angles are acute, while other 30-degree angles are obtuse.

• Not enough information to determine the truth value for the given conditional statement.

Answer explanation

The statement is false because an acute angle can measure less than 30 degrees. For example, a 20-degree angle is acute but does not measure 30 degrees, providing a counterexample.

Select the appropriate choice related to the truth value of the following conditional statement:

If an angle measures 30 degrees, then it's an acute angle.

• True. All 30-degree angles are acute angles.

• False. An angle can measure 30 degrees, but not be an acute angle. Counterexample: A 30-degree angle can be obtuse.

• False. A 30-degree angle is called a right angle, not an acute angle.

• Not enough information to determine the truth value for the given conditional statement.

Answer explanation

The statement is true because all angles measuring 30 degrees are classified as acute angles, which are defined as angles less than 90 degrees.

When taking the converse we ___________ the hypothesis and conculsion

• negate

• switch

• highlight

• switch and negate

Answer explanation

When taking the converse, we switch the hypothesis and conclusion. This means we exchange their positions, making 'switch' the correct answer. The other options do not accurately describe this process.