Download 2.1-2.4 Worksheet

Name: __________________________________________________
____o
Date: _______________ Geometry
WS 2-1 - 2-4: Geometric Reasoning
Circle the best answer.
1. What group of items is next in the pattern?
6. Given: If two angles are complementary, then both
angles measure less than 90. Angles that measure
less than 90 are acute. 1 and 2 are
complementary. What conclusion can be drawn?
A
A Only 1 is acute.
B
B Only 2 is acute.
C Both angles are acute.
2. Which conjecture is true?
D Neither angle is acute.
7. What is the next item in the pattern?
1, 2, 4, 8, …
A An even number plus 3 is always even.
B An even number plus 3 is always prime.
A 16
C 4
C An even number plus 3 is always odd.
B 4
D 16
D A prime number plus 3 is always even.
3. Given: Jennifer sings alto in the school choir. The
choir has four voice parts. The female voice parts
are soprano and alto. The male voice parts are tenor
and bass. What conclusion can be drawn?
A Jennifer sings a female voice part in the choir.
B There are no basses in the choir.
8. Which is a counterexample that shows that the
following conjecture is false: “If 1 and 2 are
supplementary, then one of the angles is obtuse”?
F m1  45 and m2  45
G m1  53 and m2  127
H m1  90 and m2  90
J m1  100 and m2  80
4. Which conditional statement is true?
9. If it is a bicycle, then it has two wheels.
Give the hypothesis of the conditional statement.
_________________________________________
_________________________________________
A If two angles are acute, then they are
complementary.
B If an angle is acute, then its measure is less
than 90.
Give the conclusion of the conditional statement.
________________________________________
________________________________________
5. What is the converse of “If there are clouds in the
sky, then it is raining”?
A If it is raining, then there are clouds in the sky.
B If it is not raining, then there are clouds in the
sky.
C If it is raining, then there are no clouds in the
sky.
D If it is not raining, then there are no clouds in the
sky.
Complete the conjecture for problems 10 and 11.
10. The sum of two odd numbers is _____________.
11. The number of sides of a polygon that has n vertices
is _______________.
Name: __________________________________________________
____o
Date: _______________
Geometry
For problems 12 - 15, show that the conjecture is false by finding a counterexample.
12. Three points on a plane always form a triangle.
(Draw a picture)
14. Every pair of supplementary angles includes
one obtuse angle. (Draw a picture)
13. For any real number x, x3 is always greater
than x2.
15. If an even number is divided by 2, then the
result is an even number.
Determine if each conditional is true. Circle True or False. If false, give a counterexample.
16. If an angle is acute, then it has a measure of
60⁰.
18. If x2 = 49, then x = 7.
True or
False → Counterexample: ___________________
True or
False → Counterexample: ___________________
19. If today is Sunday, then tomorrow is Monday.
17. If 9x – 11 = 2x +3, then x = 2.
True or
False → Counterexample: ___________________
20. If two lines intersect, then they form four right
angles.
True or
False → Counterexample: ___________________
True or
False → Counterexample: ___________________
1) Write a conditional statement from each sentence. 2) Underline the hypothesis, circle the conclusion.
3) Write the converse of the conditional.
21. Congruent segments have equal measures.
Conditional: ________________________________________________________________________________
Converse: __________________________________________________________________________________
22. You should monitor the heart rate of a patient who is ill.
Conditional: ________________________________________________________________________________
Converse: __________________________________________________________________________________