Question

1. consider the statement \if a triangle has three equal sides, then it is an equilateral triangle.\

the hypothesis is ______________________________.
the conclusion is ______________________________.

1. let ( p ) be \a shape is a triangle\ and let ( q ) be \the shape has three angles.\ combine these to write the following versions.

condition statement: ____________________________________________________.
converse: ____________________________________________________.
inverse: ____________________________________________________.
contrapositive: ____________________________________________________.

Explanation:

Step1: Identify hypothesis (If-clause)

In an "If-then" statement, the hypothesis is the part following "If".

Step2: Identify conclusion (Then-clause)

In an "If-then" statement, the conclusion is the part following "then".

Step3: Write conditional statement (If p, then q)

Combine p and q into the standard conditional structure.

Step4: Write converse (If q, then p)

Swap the positions of p and q in the conditional.

Step5: Write inverse (If not p, then not q)

Negate both p and q in the conditional.

Step6: Write contrapositive (If not q, then not p)

Negate both p and q, then swap their positions.

Answer:

For Question 8:

The hypothesis is: a triangle has three equal sides
The conclusion is: it is an equilateral triangle

For Question 9:

Condition statement: If a shape is a triangle, then the shape has three angles.
Converse: If a shape has three angles, then the shape is a triangle.
Inverse: If a shape is not a triangle, then the shape does not have three angles.
Contrapositive: If a shape does not have three angles, then the shape is not a triangle.