d Is throwing away your money in the fountain the only way of losing your money?
A
aConverse: If a pair of corresponding angles formed by two lines and a transversal are equal, then the two lines are parallel.
Converse true?: Yes
B
bConverse: In △ ABC, if angle C is 70^(∘), then the sum of angles A and B is 110^(∘).
Converse true?: Yes
C
cConverse: If lines cut by a transversal that form alternate interior angles are not parallel then those angles are not equal.
Converse true?: Yes
D
dConverse: If Johan loses money, then he throws coins in the fountain.
Converse true?: No
a Let's highlight the hypothesis and conclusion in the conditional statement.
If two lines are parallel,
then pairs of corresponding angles are equal.
The converse of a conditional statement, q→ p, exchanges the hypothesis and conclusion of the conditional statement.
If a pair of corresponding angles formed
by two lines and a transversal are equal
then the two lines are parallel.
By the Converse to the Corresponding Angles Theorem, we know that the converse is true.
b Like in Part A, we will highlight the hypothesis and conclusion in the conditional statement.
In $△ ABC$, if the sum of $m∠ A$,
and $m∠ B$ is $110^(∘)$,
then $m∠ C=70^(∘)$.
Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion.
In $△ ABC,$ if angle C is $70^(∘)$,
then the sum of angles A and B is $110^(∘)$.
By the Triangle Angle Sum Theorem, we know that the converse is true.
c Like in Parts A and B, we will highlight the hypothesis and conclusion in the conditional statement.
If alternate interior angles $k$,
and $s$ are not equal,
then the two lines cut by the
transversal are not parallel.
Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion.
If lines cut by a transversal that form
alternate interior angles are not parallel
then those angles are not equal.
By the Alternate Interior Angles Theorem, we know that the converse is true.
d Like in the previous parts, we will highlight the hypothesis and conclusion in the conditional statement.
If Johan throws coins in the fountain,
then he loses his money.
Again, to get the converse of the conditional statement, q→ p, we exchange the hypothesis and conclusion.
If Johan loses money,
then he throws coins in the fountain.
This is false as Johan could lose his money in other ways.
