Question

geometry: conditionals, converses, and biconditionals practice test

1. (1 point)

one way to show that a statement is not a good definition is to find a
a. converse
b. conditional
c. biconditional
d. counterexample

1. (1 point)

which biconditional is not a good definition?
a. a whole number is odd if and only if the number is not divisible by 2.
b. an angle is straight if and only if its measure is 180.
c. a whole number is even if and only if it is divisible by 2.
d. a ray is a bisector of an angle if and only if it splits the angle into two angles.

1. (4 points)

write the two conditional statements that form the given biconditional. then decide whether the biconditional is a good definition. explain.
three points are collinear if and only if they are coplanar.

1. (1 point)

write the two conditional statements that make up the following biconditional.
i drink juice if and only if it is breakfast time.
a. i drink juice if and only if it is breakfast time.
it is breakfast time if and only if i drink juice.
b. if i drink juice, then it is breakfast time.
if it is breakfast time, then i drink juice.
c. if i drink juice, then it is breakfast time.
i drink juice only if it is breakfast time.
d. i drink juice.
it is breakfast time.

Explanation:

12.

Un contraejemplo demuestra que una definición no es buena ya que no se cumple en todos los casos.

Un rayo que divide un ángulo en dos ángulos no necesariamente es un bisector. Un bisector divide un ángulo en dos ángulos iguales.

Las dos afirmaciones condicionales son: "Si tres puntos son colineales, entonces son coplanarios" y "Si tres puntos son coplanarios, entonces son colineales". No es una buena definición porque tres puntos pueden ser coplanarios pero no colineales.

Answer:

d. counterexample

13.