Question

unit 3 lesson 2 ee - ma.912.lt.4.3
if two angles are a linear pair, then they are adjacent.
write the converse, inverse, and contrapositive of the statement above.
converse: if two angles are adjacent, then the two angles are a linear pair.
inverse:
contrapositive:

Explanation:

1. Converse: Swap hypothesis and conclusion. Given "If \(p\) then \(q\)", the converse is "If \(q\) then \(p\)". Here \(p =\) "two angles are a linear - pair" and \(q=\) "they are adjacent", so the converse is "If two angles are adjacent, then the two angles are a linear pair".
2. Inverse: Negate both hypothesis and conclusion. The original is "If \(p\) then \(q\)", the inverse is "If not \(p\) then not \(q\)". So it is "If two angles are not a linear pair, then they are not adjacent".
3. Contrapositive: Swap and negate both hypothesis and conclusion. From "If \(p\) then \(q\)", the contrapositive is "If not \(q\) then not \(p\)". So it is "If two angles are not adjacent, then the two angles are not a linear pair".

Answer:

Converse: If two angles are adjacent, then the two angles are a linear pair.
Inverse: If two angles are not a linear pair, then they are not adjacent.
Contrapositive: If two angles are not adjacent, then the two angles are not a linear pair.