Question

1-5 reteach to build understanding conditional statements

1. a square has four congruent sides and four right angles.

write the conditional.
if a quadrilateral has four congruent sides and four
then it is a
write the converse.
if a quadrilateral is a
, then it has four congruent sides
and four
write the biconditional.
a quadrilateral is a
if and only if it has four congruent sides
and four
write the inverse.
if a quadrilateral does not have four congruent sides and four
then it is not a
write the contrapositive.
if a quadrilateral is not a
, then it does not have four congruent
sides and four

1. nicky writes, \if i am a bird, then i fly,\ as an example of a conditional

statement. also, nicky claims that the hypothesis is \i fly.\ is nicky correct?
if not, correct the error.

1. match each statement with the type of conditional.

if i am a bird, then i fly.
if i am not a bird, then i do not fly.
if i fly, then i am a bird.
if i do not fly, then i am not a bird.
i fly if and only if i am a bird.
converse
inverse
conditional
biconditional
contrapositive

Explanation:

Step1: Recall conditional - statement forms

A conditional statement is of the form "if p, then q". The converse is "if q, then p", the biconditional is "p if and only if q", the inverse is "if not p, then not q", and the contra - positive is "if not q, then not p".

Step2: Solve for the square - related statements

Conditional:

If a quadrilateral has four congruent sides and four right angles, then it is a square.

Converse:

If a quadrilateral is a square, then it has four congruent sides and four right angles.

Biconditional:

A quadrilateral is a square if and only if it has four congruent sides and four right angles.

Inverse:

If a quadrilateral does not have four congruent sides and four right angles, then it is not a square.

Contra - positive:

If a quadrilateral is not a square, then it does not have four congruent sides and four right angles.

Step3: Analyze Nicky's statement

In a conditional statement "if p, then q", p is the hypothesis and q is the conclusion. For "If I am a bird, then I fly", the hypothesis is "I am a bird", not "I fly". So Nicky is not correct.

Step4: Match the bird - related statements

"If I am a bird, then I fly." - Conditional

"If I am not a bird, then I do not fly." - Inverse

"If I fly, then I am a bird." - Converse

"If I do not fly, then I am not a bird." - Contra - positive

"I fly if and only if I am a bird." - Biconditional

Answer:

1.

• Conditional: If a quadrilateral has four congruent sides and four right angles, then it is a square.
• Converse: If a quadrilateral is a square, then it has four congruent sides and four right angles.
• Biconditional: A quadrilateral is a square if and only if it has four congruent sides and four right angles.
• Inverse: If a quadrilateral does not have four congruent sides and four right angles, then it is not a square.
• Contra - positive: If a quadrilateral is not a square, then it does not have four congruent sides and four right angles.

1. Nicky is not correct. The hypothesis of "If I am a bird, then I fly" is "I am a bird".

3.

• If I am a bird, then I fly. - Conditional
• If I am not a bird, then I do not fly. - Inverse
• If I fly, then I am a bird. - Converse
• If I do not fly, then I am not a bird. - Contra - positive
• I fly if and only if I am a bird. - Biconditional