Download Practice 6.5 Indirect Proofs

Geometry: Unit 6 - Indirect Proof
Student Practice 6.5 – Indirect Proof
Name ___________________________ Date ________________ Period ________
Pages 225-228
Write the first step of an indirect proof of the given statement.
1. It is raining outside.
2. At least one angle is obtuse.
3. XY  AB
4. m2  90
Identify the two statements that contradict each other.
5.
I. PQR is equilateral.
II. PQR is a right triangle.
II. PQR is isosceles.
6.
I. l m
II. l and m do not intersect.
III. l and m are skew.
7. Fill in the blanks to prove the following statement.
In a given triangle, LMN , there is at most one right angle.
Given:
LMN
Prove:
LMN has at most one right angle.
a.
b.
c.
d.
e.
f.
g.
h.
i.
8. Evaluate Reasonableness (1)(B) Use indirect reasoning to eliminate all but one of the following
answers. In what year was George Washington born?
A. 1492
B. 1732
C. 1902
D. 2002
9. Justify Mathematical Argumentss (1)(G) Write an indirect proof.
Given: 1  2
Prove: l
p
Assume ___________. Then 1  2 by ______________________________________ This contradicts
our given, _____________. Therefore, our assumption is _____________, and the prove ____________ is
true.
Geometry: Unit 6 - Indirect Proof
10. Given:
ABC is scalene, mABX  36 , mCBX  36
Prove: XB is not perpendicular to AC .
Assume ___________. Then BXA and BXC are right angles by def. of perpendicular. Then
BXA  BXC because ______________________________________ It is given mABX  36 ,
mCBX  36 , then ____________ because def. of congruent angles. By the Reflexive Property of
Congruence _______. So
BXA  _______ by _______. Therefore, BA  _____ by CPCTC. So,
ABC
is scalene. This contradicts our given, _____________. Therefore, our assumption is _____________, and
the prove ______________________ is true.
16. Analyze Mathematical Relationships (1)(F) Identify the two statements that contradict each other.
I. The orthocenter of JRK is on the triangle.
II. The centroid of
III.
JRK is inside the triangle.
JRK is an obtuse triangle.
17. What temporary assumption is the first step of the following indirect proof?
Given: The sides of SFK measures 3 cm, 4 cm, and 5 cm.
Prove: The orthocenter SFK is on the triangle.
A. The incenter of
SFK is inside the triangle.
B. The orthocenter of
C. The centroid of
SFK is inside the triangle.
SFK is outside the triangle.
D. The orthocenter of
SFK is inside or outside the triangle.
18. In the diagram, what are the coordinated of the circumcenter of
F. (1.5, 1.5)
H. (3, 1.5)
G. (6, 0)
KMF ?
J. (0, 0)
19. For what types of triangles are the centroid, circumcenter, incenter, and orthocenter all inside the
triangle? Explain.