1. If two angles have equal measures, then the angles are congruent.
True
False
2. Write the converse of the conditional in problem 1.
3. Is the converse from problem 2 true
Yes
No
4.Now write the bio conditional for the statement. Remember to use the phrase if and only if to combine the original and its converse.
5. What are the two conditionals that form the statement below
Two numbers are reciprocals if and only if their product is 1
6. Is the definition of a straight angle seen below reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180*
7. is the following statement a good definition? explain
a square is a figure with four right angles.
8. how can you write the statement “obtuse angles have greater measure than acute angles” so that it is a good definition?
9. which definition for a ligament did you think was better? Explain
10. write the second ligament definition above as a biconditional.
2 answers
(1) True
(2) "If two angles are congruent, then they have equal measures."
(3) True.
Step-by-step explanation: We are given the following conditional statement :
" If two angles have equal measures, then the angles are congruent."
We are to
(1) check whether the statement is true or false.
(2) write the converse of the given conditional statement.
(3) check whether the converse is true or false.
We know that
Any two angles are congruent if and only if they have equal measures.
So, the given statement is obviously true.
Also, the converse of a conditional statement "if p, then q" is "if q then p".
Therefore, the converse is
"If two angles are congruent, then they have equal measures."
Since the statement is true both ways, so the converse is also true.
Thus, the answers are
(1) True
(2) "If two angles are congruent, then they have equal measures."
(3) True.
4 answers