Q13. Draw two-line segments, KL炉聽an... [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 4: Q13. (page 150)

Draw two-line segments, $\overset{炉}{KL}$ and $\overset{炉}{MN}$ , that bisect each other at O. Mark a point P on $\overset{炉}{KN}$ and let Q be the point where $\overset{炉}{PO}$ intersects $\overset{炉}{ML}$ . Prove that O is the midpoint of $\overset{炉}{PQ}$ (First state what is given and what is to be proved.)

Short Answer

Expert verified

$螖 KNO 鈮� 螖 MLO$	SAS postulate
$\overset{炉}{MO} 鈮� \overset{炉}{ON}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 PON 鈮� 螖 QOM$	ASA postulate
O is the midpoint of $\overset{炉}{PQ}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Draw a diagram.

Draw a diagram with given instructions.

Draw two-line segments, $\overset{炉}{K L} and \overset{炉}{M N}$ that bisect each other at $O$ . Mark a point $P$ on $\overset{炉}{K N}$ and let $Q$ be the point where $\overset{炉}{P Q}$ intersects $\overset{炉}{M L}$ .

Step 2. Description of step.

Consider $\overset{炉}{K O} 鈮� \overset{炉}{O N}, \overset{炉}{M O} 鈮� \overset{炉}{O N}$ and $鈭� K O N 鈮� 鈭� M O L$ then by SAS postulate, $螖 K N O 鈮� 螖 M L O$ .

Step 3. Description of step.

Consider $螖 P O N$ and $螖 Q O M$ in which $\overset{炉}{M O} 鈮� \overset{炉}{O N}$ , $鈭� M O Q 鈮� 鈭� P O N$ as they are vertically opposite angle and $鈭� P N O 鈮� 鈭� O M Q$ then by ASA postulate, $螖 P O N 鈮� 螖 Q O M$ .

Step 4. Description of step.

As $螖 P O N 鈮� 螖 Q O M$ by the corresponding parts of congruent triangles, $\overset{炉}{P O} 鈮� \overset{炉}{Q O}$ . Which implies that $O$ is the midpoint of $\overset{炉}{P Q}$ .

Step 5. Key steps of a proof.

Make a list of key steps of a proof.

$螖 K N O 鈮� 螖 M L O$	SAS postulate
$\overset{炉}{M O} 鈮� \overset{炉}{O N}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 P O N 鈮� 螖 Q O M$	ASA postulate
$O$ is the midpoint of $\overset{炉}{P Q}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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Short Answer

Step by step solution

Step 1. Draw a diagram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Key steps of a proof.

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91影视

Draw two-line segments, KL炉and MN炉, that bisect each other at O. Mark a point P onKN炉 and let Q be the point wherePO炉intersects ML炉. Prove that O is the midpoint of PQ炉(First state what is given and what is to be proved.)

Short Answer

Step by step solution

Step 1. Draw a diagram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Key steps of a proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.