Question

Complete the proof $KM>NP$if given is $KL>NL$and $LM>LP$.

Short answer

$KL>NL$ $LM>LP$	Given
$KL+LM>NL+LP$	From the property of inequality.
$\begin{array}{l}KL+LM=KM\\ NL+LP=NP\end{array}$	Segment addition postulate
$KM>NP$	Substitution property.

Step-by-step solution

Step 1. Property of inequality

If $a>b$and$c\ge d$ then $a+c>b+d$.

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

Since $KL>NL$and $LM>LP$then from the property of inequality $KL+LM>NL+LP$.

Step 3. Prove that KM > NP

Proof:

Since $KL+LM>NL+LP$ …… (1)

From Segment addition postulate

$\begin{array}{l}KL+LM=KM\\ NL+LP=NP\end{array}$ …… (2)

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

$KM>NP$

Hence proved $KM>NP$.