siven: ALMN; mLL > m2N rove: MN > TM
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Prove that one side is greater than the other side by completing the two column proof below
![ACTIVITY 3. PROVING:
Direction: Prove that one side is greater than the other side by
completing the two-column proof below.
Given: ALMN; mLL > mLN
L.
Prove: MN > LM
Proof:
Indirect Proof: Assume MN LM
Statements
Reasons
MN
1.
= LM or
MN
LM
1. By assumption
MN
2. Considering
LM
: If
MN
LM
2.Definition of
then
3. Base angles of isosceles As
are congruent
3. L -
4. The conclusion that
7.
4. The assumption MN TMis
7.
the given that
5.
Theorem
MN
5. Considering
LM
MN
If
LM
7.
Then m
< m
6. The conclusion that m
6. The assumption
is
The given that m
L>m
7.The assumption that
contradicts the known fact that m
7. Therefore,
must be
> m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4325ae0-60aa-457f-a131-6a298c3e6bd0%2F512ddf7c-6923-4523-8138-79a5ddd87e34%2Fvb1eq33_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ACTIVITY 3. PROVING:
Direction: Prove that one side is greater than the other side by
completing the two-column proof below.
Given: ALMN; mLL > mLN
L.
Prove: MN > LM
Proof:
Indirect Proof: Assume MN LM
Statements
Reasons
MN
1.
= LM or
MN
LM
1. By assumption
MN
2. Considering
LM
: If
MN
LM
2.Definition of
then
3. Base angles of isosceles As
are congruent
3. L -
4. The conclusion that
7.
4. The assumption MN TMis
7.
the given that
5.
Theorem
MN
5. Considering
LM
MN
If
LM
7.
Then m
< m
6. The conclusion that m
6. The assumption
is
The given that m
L>m
7.The assumption that
contradicts the known fact that m
7. Therefore,
must be
> m
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