Converse
Statements
Mathematics 3204/05
1.
Converse Statements
Which statement has a converse that must also be true?
(A)
(B)
(C)
(D)
2.
Public Exam Questions
If a quadrilateral is a square, then it has four congruent sides.
If a quadrilateral is a square, then it is a rectangle.
If a triangle is equilateral, then it has three congruent sides.
If two triangles are congruent, then corresponding angles are congruent.
Which is the converse of:
“If two chords of a circle are congruent, then they are equidistant from the
centre.”
(A)
(B)
(C)
(D)
3.
What is the converse of: “If two chords of a circle are parallel, then the two arcs
between the chords are congruent.”?
(A)
(B)
(C)
(D)
4.
If two chords are parallel, then they are congruent.
If two chords are perpendicular bisectors of one another, then they are
equidistant from the centre.
If two chords of a circle pass through the centre, then they are congruent.
If two chords of a circle are equidistant from the centre, then they are
congruent.
If the two arcs between the chords in a circle are congruent, then the
chords are not parallel.
If the two arcs between the chords in a circle are not congruent, then the
chords are not parallel.
If the two arcs between the chords in a circle are congruent, then the
chords are parallel.
If two chords of a circle are not parallel, then the arcs between the chords
are not congruent.
What is the converse of the following statement?
“If a diameter of a circle intersects a chord of the circle at right angles, then it
bisects the chord.”
(A)
(B)
(C)
(D)
If a diameter bisects a chord of the circle, then it intersects the chord at
right angles.
If a diameter of a circle intersects a chord of the circle, then it does not
intersect the chord at right angles.
If a diameter of a circle does not bisect a chord of the circle, then it does
not intersect the chord at right angles.
All diameters of a circle bisect chords at right angles.
Labrador School Board
274
2007-2008
Mathematics 3204/05
5.
Public Exam Questions
Converse Statements
Which is the converse of:
“If a diameter bisects an inscribed angle in a circle, then the diameter
bisects the arc subtending the inscribed angle.” ?
6.
(A)
If a diameter bisects an inscribed angle in a circle, then the arc subtending
the inscribed angle bisects the diameter.
(B)
If the diameter of a circle bisects the arc subtending an inscribed angle,
then the diameter bisects the inscribed angle.
(C)
If a line bisects an arc subtending an inscribed angle, then it bisects the
inscribed angle in the circle.
(D)
If the diameter of a circle does not bisect the arc subtending an inscribed
angle, then the diameter does not bisect the inscribed angle.
Which is the converse of: “If all vertices of a quadrilateral are on a circle, then it
is a cyclic quadrilateral.”?
(A)
(B)
(C)
(D)
7.
Which is the converse of: “Two minor arcs are congruent if their central angles
are congruent.”?
(A)
(B)
(C)
(D)
8.
All vertices of a quadrilateral are on a circle iff it is a cyclic quadrilateral.
If all vertices of a quadrilateral are not on a circle, then the quadrilateral is
not cyclic.
If a quadrilateral is cyclic, then all vertices are not on a circle.
If a quadrilateral is cyclic, then all vertices are on a circle.
Two minor arcs are not congruent iff their central angles are not
congruent.
Two central angles are congruent if their minor arcs are congruent.
Two central angles are not congruent if their minor arcs are congruent.
Two minor arcs are congruent iff their central angles are congruent.
Which is the converse of: “If a quadrilateral is inscribed in a circle, then opposite
angles are supplementary.”?
(A)
(B)
(C)
(D)
If opposite angles in a quadrilateral are not supplementary, then the
quadrilateral is inscribed in a circle.
If opposite angles in a quadrilateral are not supplementary, then the
quadrilateral is not inscribed in a circle.
If opposite angles in a quadrilateral are supplementary, then the
quadrilateral is inscribed in a circle.
If opposite angles in a quadrilateral are supplementary, then the
quadrilateral is not inscribed in a circle.
Labrador School Board
275
2007-2008
Mathematics 3204/05
9.
Converse Statements
Which is the converse of, “If the vertices of a quadrilateral lie on a circle, then
that quadrilateral is cyclic.”?
(A)
(B)
(C)
(D)
10.
Public Exam Questions
If a quadrilateral is cyclic, then the vertices of that quadrilateral lie on a
circle.
If a quadrilateral is not cyclic, then the vertices of that quadrilateral do not
lie on a circle.
If the vertices of a quadrilateral do not lie on a circle, then that
quadrilateral is not cyclic.
If the vertices of a quadrilateral lie on a circle, then that quadrilateral is not
cyclic.
“If a point lies on the bisector of an angle, then that point is equidistant from the
sides of the angle.” What is the converse of this statement?
(A)
(B)
(C)
(D)
If a point does not lie on the bisector of an angle, then that point is
equidistant from the sides of the angle.
If a point does not lie on the bisector of an angle, then that point is not
equidistant from the sides of the angle.
If a point is equidistant from the sides of an angle, then that point does not
lie on the bisector of the angle.
If a point is equidistant from the sides of an angle, then that point lies on
the bisector of the angle.
Labrador School Board
276
2007-2008
Mathematics 3204/05
Public Exam Questions
Converse Statements
Answers Converse Statements
1. C
2. D
3. C
4. A
5. C
6. D
7. B
8. C
9. A
10. D
Labrador School Board
277
2007-2008