Q8. Complete the proof KM>NP聽if ... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

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 $c 鈮� d$ 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 $K L + L M > N L + L P$ 鈥︹€� (1)

From Segment addition postulate

$\begin{array}{l} K L + L M = K M \\ N L + L P = N P \end{array}$ 鈥︹€� (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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91影视

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

One App. One Place for Learning.

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91影视

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

Geometry

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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