very simple.
1.
The conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.
If x = 12, then 2x-5 = 19.
O a
If 2x – 5 = 19, then x = 12. True statement. Biconditional: x = 12 if and only if 2x – 5 = 19.
Ob
If x = 12, then 2x – 5 = 19. False statement.
Oc
If 2x – 5 = 19, then x = 12. False statement.
O a
Ob
Oc
2.
The conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.
If x = 3, then x = 3.
If x| = 3, then x = 3. False statement.
0 а
Ob
oc
If x = 3, then [x] = 3. False statement.
If x = 3, then x = 3. True statement. Biconditional: x = 3 if and only if x = 3.
3.
Test the statement below to see if it is reversible. If so, write it as a true biconditional. If not, choose not reversible.
Parallel planes are planes that do not intersect.
O a
Ob
OC
Not reversible.
If planes are parallel, then they do not intersect.
Planes are parallel if and only if they do not intersect.
O a
Ob
Ос
4
Test the statement below to see if it is reversible. If so, write it as a true biconditional. If not, choose not reversible.
A rectangle is a four-sided figure with at least one right angle.
о а
Ob
O
C
Od
A four-sided figure is a rectangle if and only if it has at least one right angle.
A rectangle is a four-sided figure if and only if it has at least one right angle.
If a rectangle is a four-sided figure, then it has at least one right angle.
Not reversible.
5.
Is the statement below a good definition? Explain.
A cat is an animal with whiskers.
a
Yes, this is a good definition.
b
No, other animals could fit this definition.
оа
Oь
6
Is the statement below a good definition? Explain.
A perpendicular bisector is a line, segment or ray that is perpendicular to a segment at its midpoint and divides the segment into
two congruent segments.
O a
Ob
No, other geometric parts could fit this definition.
Yes, this is a good definition.
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