Question

lesson 5 homework
period 5th
complete each table for the conditional statement.
if an angle is classified as a right angle, then it has a measure of 90°.

	relationship to conditional	statement	true or false
2.	inverse
3.	contrapositive
4.	write the conditional using \if and only if\.

Explanation:

1. Converse

Step1: Recall converse definition

The converse of a conditional statement "If \( p \), then \( q \)" is "If \( q \), then \( p \)". Here, \( p \): "an angle is classified as a right angle", \( q \): "it has a measure of \( 90^\circ \)".

Step2: Formulate converse

So the converse statement is: "If an angle has a measure of \( 90^\circ \), then it is classified as a right angle."

Step3: Determine truth value

By definition, a right angle is an angle with measure \( 90^\circ \), so this is True.

2. Inverse

Step1: Recall inverse definition

The inverse of "If \( p \), then \( q \)" is "If not \( p \), then not \( q \)".

Step2: Formulate inverse

So the inverse statement is: "If an angle is not classified as a right angle, then it does not have a measure of \( 90^\circ \)."

Step3: Determine truth value

An angle not a right angle (e.g., acute, obtuse) can't be \( 90^\circ \), so this is True.

3. Contrapositive

Step1: Recall contrapositive definition

The contrapositive of "If \( p \), then \( q \)" is "If not \( q \), then not \( p \)".

Step2: Formulate contrapositive

So the contrapositive statement is: "If an angle does not have a measure of \( 90^\circ \), then it is not classified as a right angle."

Step3: Determine truth value

If an angle isn't \( 90^\circ \), it's not a right angle, so this is True.

4. Biconditional (If and only if)

Answer:

Step1: Recall biconditional definition

A biconditional " \( p \) if and only if \( q \)" means \( p \to q \) and \( q \to p \) (converse is true, so we can write it).

Step2: Formulate biconditional

Using the original \( p \) and \( q \), the statement is: "An angle is classified as a right angle if and only if it has a measure of \( 90^\circ \)."

Filled Table:

	Relationship to Conditional	Statement	True or False
2	Inverse	If an angle is not classified as a right angle, then it does not have a measure of \( 90^\circ \).	True
3	Contrapositive	If an angle does not have a measure of \( 90^\circ \), then it is not classified as a right angle.	True
4	-	An angle is classified as a right angle if and only if it has a measure of \( 90^\circ \).	-