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
right - angles, 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", where p is the hypothesis and q is the conclusion.

Step2: Write the conditional for the square

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

Step3: Write the converse

The converse of "if p, then q" is "if q, then p". So, if a quadrilateral is a square, then it has four congruent sides and four right - angles.

Step4: Write the biconditional

The biconditional is "p if and only if q". A quadrilateral is a square if and only if it has four congruent sides and four right - angles.

Step5: Write the inverse

The inverse of "if p, then q" is "if not p, then not q". If a quadrilateral does not have four congruent sides and four right - angles, then it is not a square.

Step6: Write the contrapositive

The contrapositive of "if p, then q" is "if not q, then not p". If a quadrilateral is not a square, then it does not have four congruent sides and four right - angles.

Step7: Analyze Nicky's statement

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

Step8: Match the bird - related statements

• "If I am a bird, then I fly" is a conditional statement.
• "If I am not a bird, then I do not fly" is an inverse statement.
• "If I fly, then I am a bird" is a converse statement.
• "If I do not fly, then I am not a bird" is a contrapositive statement.
• "I fly if and only if I am a bird" is a biconditional statement.

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.
• Contrapositive: 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 the conditional statement "if I am a bird, then I fly" is "I am a bird", not "I fly".

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" - Contrapositive
• "I fly if and only if I am a bird" - Biconditional