Geometry
(G.3) Geometric Structure. The student applies logical reasoning to justify and prove mathematical statements. The student
is expected to: (A) determine the validity of a conditional statement, its converse, inverse and contrapositive.
G.3A Mini-Assessment
1. Given: If an angle measures more than 90° , then the angle is an obtuse angle. What is the
hypothesis of the statement?
A
The angle is obtuse.
B
The angle is not obtuse.
C
The angle measures less than 90° .
D The angle measures more than 90° .
2. “Ten is a multiple of 5.” written as a conditional isF
If the number is not 5, then it is a multiple of 10.
G If the number is a multiple of 5, then it is 10.
H If the number is 10, then it is a multiple of 5.
J
If the number is 5, then it is a multiple of 10.
3. The contrapositive of “If three points are collinear, then they lie on a line” isA
If three points are collinear, then they do not lie on a line.
B
If three points, A, B and C, lie on a line, then they are collinear.
C
If three points do not lie on a line, then they are non-collinear.
D If three points are non-collinear, then they do not lie on a line.
4. Given: If this is January, then it is the first month of the year.
Which of the following is the converse of this conditional?
F
If this is the first month of the year, then it is January.
G If it is not January, then it is not the first month of the year.
H If it is February, then it is not January.
J
January is the first month of the year.
TEKSING TOWARD STAAR © 2012
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Geometry
(G.3) Geometric Structure. The student applies logical reasoning to justify and prove mathematical statements. The student
is expected to: (A) determine the validity of a conditional statement, its converse, inverse and contrapositive.
5. Which of the following shows the correct truth table for the inverse of p  q
A
B
p
T
T
F
F
q
F
T
T
T
p
T
T
F
F
q
F
F
T
T
p
q
p q
p
q
p q
F
F
T
T
F
F
T
T
T
F
F
F
T
T
F
F
T
T
F
F
T
T
F
F
C
D
p
T
T
F
F
q
F
T
T
F
p
T
T
F
F
q
F
T
F
T
p
q
p q
p
q
p q
F
F
T
T
F
F
T
T
T
F
F
T
T
F
F
T
T
T
F
T
T
T
F
T
6. Given: If a figure is a square, then the figure is a parallelogram. Which of the following
related conditionals will be true?
F
The contrapositive only
G The contrapositive and the inverse
H The inverse and the converse
J
The inverse only
7. Which of the following conditionals have a converse conditional that is true?
A
If a triangle is an obtuse triangle, then it will contain two acute angles.
B
If a triangle is an obtuse triangle, then it will not contain a right angle.
C
If a quadrilateral is a square, then the quadrilateral is a rectangle.
D If three points are non-collinear, then they do not lie on a line.
TEKSING TOWARD STAAR © 2012
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Geometry
(G.3) Geometric Structure. The student applies logical reasoning to justify and prove mathematical statements. The student
is expected to: (A) determine the validity of a conditional statement, its converse, inverse and contrapositive.
8. Which of the following is a biconditional?
F
If this is Sunday, then it is the first day of the week.
G This is the first day of the week if and only if it is Sunday.
H If this is the first day of the week, then it is Sunday.
J
If this is not Sunday, then it is not the first day of the week.
9. Which of the following will correctly complete the following conditional?
If triangle ABC has vertices A(4, 2), B(6, -1) and C( -1, 3), then the triangle is a(n) 
A
right triangle.
B
equilateral triangle.
C
isosceles triangle.
D scalene triangle.
10. If a conditional, p  q , is true, then which of the following must be true also?
F
Contrapositive
G Converse and Inverse
H Converse
J
Inverse
TEKSING TOWARD STAAR © 2012
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