Question

Jenni wrote a conditional statement and its converse. Conditional: If angles are right angles, then the angles have the same measure. Converse: If angles have the same measurement, then they are right angles. Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.

Answer 1

Jenni wrote the statement properly.

The converse is wrong. A counterexample to the converse is two vertical angles whose measures are 46°, since they have the same measure, but are not right angles.

Explanation:

How to Write a Converse Statement:

• Jenni wrote the converse statement properly.

We can think of the conditional statement as in terms of p and q:

Conditional statement = "if p, then q".

• In this case, "if angles are right angles" is p and "the angles have the same measure is q".

• Since the converse statement is "if q, then p", the converse to Jenni's conditional statement is: if angles have the same measure, then they are right angles.

• In order for a converse to be true, it must always be true and can't have any counterexamples.

Validity of Jenni's Converse Statement:

• However, the converse is false.

• A converse is only true if it's always true--this means it can't have any counterexamples.

• A counterexample to the converse is two vertical angles whose measures are 46°, since vertical angles have the same measure, but our two angles are not right angles.