Question

1. the triangle is equilateral. → negation:
2. two lines are parallel. → negation:
3. the angle measures 90 degrees. → negation:
4. a square has four sides. → negation:
5. the shape is a rectangle. → negation:

part d. write the conditional, converse, inverse, and contrapositive forms. then, write whether each statement is true or false.
statement: two lines are perpendicular if they intersect to form right angles.

statement type	statement	true or false
converse
inverse
contrapositive

Explanation:

Step1: Define negation

Negation is making a statement false.

Step2: Find negation of "The triangle is equilateral"

The triangle is not equilateral.

Step3: Find negation of "Two lines are parallel"

Two lines are not parallel.

Step4: Find negation of "The angle measures 90 degrees"

The angle does not measure 90 degrees.

Step5: Find negation of "A square has four sides"

A square does not have four sides (false statement in reality but correct negation).

Step6: Find negation of "The shape is a rectangle"

The shape is not a rectangle.

Step7: Analyze conditional statement "Two lines are perpendicular if they intersect to form right - angles"

Conditional: If two lines intersect to form right angles, then they are perpendicular. (True)
Converse: If two lines are perpendicular, then they intersect to form right angles. (True)
Inverse: If two lines do not intersect to form right angles, then they are not perpendicular. (True)
Contrapositive: If two lines are not perpendicular, then they do not intersect to form right angles. (True)

Answer:

1. The triangle is not equilateral.
2. Two lines are not parallel.
3. The angle does not measure 90 degrees.
4. A square does not have four sides.
5. The shape is not a rectangle.

Conditional: If two lines intersect to form right angles, then they are perpendicular. True
Converse: If two lines are perpendicular, then they intersect to form right angles. True
Inverse: If two lines do not intersect to form right angles, then they are not perpendicular. True
Contrapositive: If two lines are not perpendicular, then they do not intersect to form right angles. True