siven: ALMN; mLL > m2N rove: MN > TM

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 41E
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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
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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