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Complete the proof KM>NPif given is KL>NLand LM>LP.

Short Answer

Expert verified

KL>NL

LM>LP


Given

KL+LM>NL+LP

From the property of inequality.

KL+LM=KMNL+LP=NP

Segment addition postulate

KM>NP

Substitution property.

Step by step solution

01

Step 1. Property of inequality

If a>bandcd then a+c>b+d.

02

Step 2. Show that KL + LM > NL + LP

Since KL>NLand LM>LPthen from the property of inequality KL+LM>NL+LP.

03

Step 3. Prove that KM > NP

Proof:

Since KL+LM>NL+LP …… (1)

From Segment addition postulate

KL+LM=KMNL+LP=NP …… (2)

Now, substitute the results of equation (2) in equation (1) therefore

KM>NP

Hence proved KM>NP.

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