1. ## Converses

I. WRITE the converse of each statement. Try to decide whether each statement, and each converse, it true or false.

1. If clouds cover the sky, you cannot see the moon.

2. You see lions and elephants if you are in Africa.
MY ANSWER: FALSE: IF YOU CAN SEE THE LION AND ELEPHANT THEN YOU ARE IN AFRICA.

3. Anyone who has scarlet fever is seriously ill.

4. IF two angles are congruent, they are right angles.
5. If two angles form a linear pair, then they are supplementary.
6. Two angles are each acute if they are complementary.

II. Is a converse of every true statement true? justify your answer?
III. May a converse of a false statement be true? justify your answer?

thanks

2. It's very simple. The converse of "If P, then Q" is "If Q, then P".

1. If clouds cover the sky, you cannot see the moon.
The converse is, "If you cannot see the moon, then clouds cover the sky."

2. You see lions and elephants if you are in Africa.
MY ANSWER: FALSE: IF YOU CAN SEE THE LION AND ELEPHANT THEN YOU ARE IN AFRICA.
I agree, but I would write "see lions and elephants," exactly as in the original sentence, instead of "can see the lion and elephant." Your variant introduces some complications, such as when you can see lions but don't.

3. Anyone who has scarlet fever is seriously ill.
This can be rewritten as, "For every person x, if x has scarlet fever, then x is seriously ill." The converse is "For every person x, if x is seriously ill, then x has scarlet fever," or "Anyone who is seriously ill has scarlet fever."

Try 4, 5, 6 and post the results if you'd like.

II. Is a converse of every true statement true? justify your answer?
Consider I.3.
III. May a converse of a false statement be true? justify your answer?
Consider I.4.

3. 4. IF two angles are congruent, they are right angles. FALSE>>>>>please check
CONVERSE: If two angles are right angles,then they are congruent angles.
5. If two angles form a linear pair, then they are supplementary.FALSE>>>>>please check
CONVERSE: iF two angles are supplementary, then two angles form linear pair.
6. Two angles are each acute if they are complementary.TRUE>>>>>please check
CONVERSE: Two angles are complementary angles, if they are acute....
please try to check my work

pleae t

4. 4. IF two angles are congruent, they are right angles. FALSE>>>>>please check
CONVERSE: If two angles are right angles,then they are congruent angles.
Correct. The converse is true.

5. If two angles form a linear pair, then they are supplementary.FALSE>>>>>please check
CONVERSE: iF two angles are supplementary, then the two angles (or they) form linear pair.
This page says that the original statement is true. Do you have a different definition? The converse is false.

6. Two angles are each acute if they are complementary.TRUE>>>>>please check
CONVERSE: Two angles are complementary angles, if they are acute....
please try to check my work
Correct. The converse is false.

5. Thank you so much for your help. God bless