Question

1. fill in the blanks to complete the alternate forms of the given statement: \if an angle measures 90 degrees, then the angle is a right angle.\ converse: if an angle \\(\square\\), then the angle \\(\square\\). inverse: if an angle does \\(\square\\), then the angle is \\(\square\\). contrapositive: if an angle is \\(\square\\), then the angle does \\(\square\\).

Explanation:

Converse:

To form the converse of a conditional statement "If \(p\), then \(q\)", we switch the hypothesis (\(p\)) and the conclusion (\(q\)). Here, \(p\) is "an angle measures 90 degrees" and \(q\) is "the angle is a right angle". So the converse is "If \(q\), then \(p\)".

Inverse:

To form the inverse of a conditional statement "If \(p\), then \(q\)", we negate both the hypothesis (\(p\)) and the conclusion (\(q\)). So we get "If not \(p\), then not \(q\)".

Contrapositive:

To form the contrapositive of a conditional statement "If \(p\), then \(q\)", we negate both the hypothesis and the conclusion and then switch them. So it is "If not \(q\), then not \(p\)".

Answer:

Converse:

If an angle \(\boldsymbol{\text{is a right angle}}\), then the angle \(\boldsymbol{\text{measures 90 degrees}}\).

Inverse:

If an angle does \(\boldsymbol{\text{not measure 90 degrees}}\), then the angle is \(\boldsymbol{\text{not a right angle}}\).

Contrapositive:

If an angle is \(\boldsymbol{\text{not a right angle}}\), then the angle does \(\boldsymbol{\text{not measure 90 degrees}}\).