Question

1. ellen claims that both this conditional statement and its converse are true. if a polygon is a rectangle, then it has right angles. a. write the converse of the conditional. b. only one of the statements is true. determine which statement is false and provide a counterexample to support your answer. 10. in lewis carroll’s alice’s adventures in wonderland, the mad hatter states: “why you might just as well say that ‘i see what i eat’ is the same thing as ‘i eat what i see’!” a. write “i see what i eat” as a conditional statement. b. write “i eat what i see” as a conditional statement. c. explain why the mad hatter is wrong. 11. which conditional statement has a false converse? a. if two planes are parallel, then they have no points in common. b. if a figure is a square, then it has four sides. c. if a point has x - coordinate 0, then it lies on the y - axis. d. if two angles are congruent, then they have the same measure. e. none 12. which statement has a true converse? a. if a vehicle is a car, then it has four wheels. b. if you go to asia from the united states, then you cross an ocean. c. if you own a dog, then your pet is furry. d. if you are at least 16 years old, then you are old enough to drive alone. e. none

Explanation:

9.

a.

To find the converse, we swap the hypothesis and conclusion. The original is "If a polygon is a rectangle, then it has right - angles". So the converse is "If a polygon has right angles, then it is a rectangle".

The original statement "If a polygon is a rectangle, then it has right angles" is true by the definition of a rectangle. The converse "If a polygon has right angles, then it is a rectangle" is false. A counter - example is a right - angled trapezoid which has right angles but is not a rectangle.

A conditional statement is of the form "If p, then q". For "I see what I eat", it can be written as "If I eat something, then I see it".

Answer:

If a polygon has right angles, then it is a rectangle.

b.