Chapter 6: Q8. (page 207)

Complete the proof $K M > N P$ if given is $K L > N L$ and $L M > L P$ .

Short Answer

Expert verified

$K L > N L$ $L M > L P$	Given
$K L + L M > N L + L P$	From the property of inequality.

$\begin{array}{l} K L + L M = K M \\ N L + L P = N P \end{array}$	Segment addition postulate
$K M > N P$	Substitution property.

Step by step solution

Step 1. Property of inequality

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

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

Since $K L > N L$ and $L M > L P$ then from the property of inequality $K L + L M > N L + L P$ .

Step 3. Prove that KM > NP

Proof:

Since $K L + L M > N L + L P$ …… (1)

From Segment addition postulate

$\begin{array}{l} K L + L M = K M \\ N L + L P = N P \end{array}$ …… (2)

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

$K M > N P$

Hence proved $K M > N P$ .

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Complete the proof $K M > N P$ if given is $K L > N L$ and $L M > L P$ .

Short Answer

Step by step solution

Step 1. Property of inequality

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

Step 3. Prove that KM > NP

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

Short Answer

Step by step solution

Step 1. Property of inequality

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

Step 3. Prove that KM > NP

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Complete the proof $K M > N P$ if given is $K L > N L$ and $L M > L P$ .