Question

(b) problem 13: (first taught in lesson 48) read the true statement below and then tell whether its converse, inverse, and contrapositive are also true. if two angles are a linear pair, then they are supplementary. converse inverse contrapositive if two angles are supplementary, then they are a linear pair. true false go

Explanation:

Step1: Define converse, inverse, contrapositive

Let the original statement be “If \(p\) (two angles are a linear pair), then \(q\) (they are supplementary)”.

• Converse: “If \(q\), then \(p\)”
• Inverse: “If not \(p\), then not \(q\)”
• Contrapositive: “If not \(q\), then not \(p\)”

Step2: Analyze converse

For the converse “If two angles are supplementary, then they are a linear pair”.
Counter - example: Two non - adjacent angles of measure \(100^{\circ}\) and \(80^{\circ}\) are supplementary but not a linear pair. So converse is false.

Step3: Analyze inverse

The inverse is “If two angles are not a linear pair, then they are not supplementary”.
Counter - example: Two non - adjacent angles of measure \(100^{\circ}\) and \(80^{\circ}\) are not a linear pair but are supplementary. So inverse is false.

Step4: Analyze contrapositive

The contrapositive is “If two angles are not supplementary, then they are not a linear pair”.
By the definition of a linear pair (sum of angles in a linear pair is \(180^{\circ}\)), if the sum of two angles (\(
eq180^{\circ}\), i.e., not supplementary), they cannot be a linear pair. So contrapositive is true.

Answer:

Converse: False; Inverse: False; Contrapositive: True