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Converse Statements
Converse – A statement formed by interchanging the subject and predicate. The converse of a true
statement may be true or false. To argue from a true statement to the truth of its converse is not valid.
Examples:
1. If Sam lives in Prince Edward Island, then she lives in the smallest Canadian province.
The converse is:
If Sam lives in the smallest Canadian province, then she lives in Prince Edward Island.
In this case, the statement and its converse are true. But this is not always the case!
2. If it is raining, then the grass must be wet. (TRUE)
Converse: If the grass is wet, then it must be raining. (FALSE – it could have been a sprinkler…)
3. If a triangle has three equal angles, then it is equilateral. (TRUE)
Converse: If a triangle is equilateral, then it has three equal angles. (TRUE)
When both the statement and converse are true, can rewrite using “IFF”. IFF = “If and only if”
A triangle has three equal angles IFF it is equilateral.
4. If two chords are equidistant from the centre of a circle, then the chords are congruent.
Converse: If two chords are congruent, then the chords are equidistant from the centre of the circle.
Both statements are true, so can rewrite using IFF:
Two chords are equidistant from the centre of a circle IFF the chords are congruent.
PRACTICE:
1. What point is equidistant from all points that lie on a circle?
2. What is the greatest possible distance between two points which lie on a circle with radius R?
3. Write the converse of the following statements. If both statements are true, rewrite using IFF.
(a) If you attend Citadel High School, then you live in Nova Scotia.
(b) If it is night time, then you cannot see the sun.
(c) If a shape has three sides, then it is a triangle.
(d) If a shape is a square, then it has four sides.
(e) If two or more circles are congruent, then they have the same radius.
4. Complete questions pg. 211 #12, 13, 15, 17, 19, 20
Converse Statements
Converse – A statement formed by interchanging the subject and predicate. The converse of a true
statement may be true or false. To argue from a true statement to the truth of its converse is not valid.
Examples:
1. If Sam lives in Prince Edward Island, then she lives in the smallest Canadian province.
The converse is:
If Sam lives in the smallest Canadian province, then she lives in Prince Edward Island.
In this case, the statement and its converse are true. But this is not always the case!
2. If it is raining, then the grass must be wet. (TRUE)
Converse:
3. If a triangle has three equal angles, then it is equilateral. (TRUE)
Converse:
When both the statement and converse are true, can rewrite using “IFF”. IFF = “If and only if”
A triangle has three equal angles IFF it is equilateral.
4. If two chords are equidistant from the centre of a circle, then the chords are congruent.
Converse:
Both statements are true, so can rewrite using IFF:
PRACTICE:
1. What point is equidistant from all points that lie on a circle?
2. What is the greatest possible distance between two points which lie on a circle with radius R?
3. Write the converse of the following statements. If both statements are true, rewrite using IFF.
(a) If you attend Citadel High School, then you live in Nova Scotia.
(b) If it is night time, then you cannot see the sun.
(c) If a shape has three sides, then it is a triangle.
(d) If a shape is a square, then it has four sides.
(e) If two or more circles are congruent, then they have the same radius.
4. Complete questions pg. 211 #12, 13, 15, 17, 19, 20