Download Mathematics 3204

Mathematics 3204/05
1.
Which statement has a converse that must also be true?
(A)
(B)
(C)
(D)
2.
Converse Statements
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.
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Mathematics 3204/05
5.
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.
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Mathematics 3204/05
9.
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.
(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.
If two triangles are congruent, then their corresponding sides and corresponding angles are
equal. What is the converse of this statement?
(A)
(B)
(C)
(D)
12.
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)
11.
Converse Statements
If corresponding sides and corresponding angles of a triangle are equal, then the
triangles are congruent.
If corresponding sides and corresponding angles of a triangle are not equal, then the
triangles are congruent.
If two triangles are congruent, then their corresponding sides and corresponding
angles are not equal.
If two triangles are not congruent, then their corresponding sides and corresponding
angles are not equal.
If two sides of a triangle are congruent, then the angles opposite the congruent sides are
congruent. What is the converse of this statement?
(A)
(B)
(C)
(D)
If two angles of a triangle are congruent, then the sides opposite the congruent angles
are congruent.
It two angles of a triangle are congruent, then the sides opposite the congruent angles
are not congruent.
If two sides of a triangle are congruent, then the angles opposite these sides are not
congruent.
If two sides of a triangle are not congruent, then the angles opposite these sides are not
congruent.
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Mathematics 3204/05
13.
Converse Statements
What is the converse of the statement, “If a triangle is isosceles then the base angles are
congruent”?
(A)
(B)
(C)
(D)
A triangle is isosceles iff the two base angles are congruent.
If a triangle is not isosceles then the base angles are not congruent.
If the base angles of a triangle are congruent then the triangle is isosceles.
The two base angles of a triangle are congruent iff the triangle is isosceles.
Question
Answer
1
C
2
D
3
C
4
A
5
B
6
D
7
B
8
C
9
A
10
D
11
A
12
A
13
C
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