Q12. Write proofs in the form specifi... [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: Q12. (page 150)

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).
12. Given: $\overset{炉}{PQ} 鈯� \overset{炉}{QR}; \overset{炉}{PS} 鈯� \overset{炉}{SR}; \overset{炉}{PQ} 鈮� \overset{炉}{PS}$
Prove: O is the midpoint of $\overset{炉}{QS}$ .

Short Answer

Expert verified

$螖 PQR 鈮� 螖 PSR$	HL postulate
$鈭� QRP 鈮� 鈭� SRP$ ; $\overset{炉}{QR} 鈮� \overset{炉}{SR}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 QRO 鈮� 螖 SRO$	SAS postulate
O is the midpoint of $\overset{炉}{QS}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Description of step.

Consider $螖 P Q R$ and $螖 P S R$ . From the given figure it can be observed that $\overset{炉}{P Q} 鈮� \overset{炉}{P S}$ which are legs and $\overset{炉}{P R} 鈮� \overset{炉}{P R}$ which is hypotenuse then by HL postulate, $螖 P Q R 鈮� 螖 P S R$ .

Step 2. Description of step.

As $螖 P Q R 鈮� 螖 P S R$ then by corresponding parts of congruent triangles, $鈭� Q R P 鈮� 鈭� S R P$ and $\overset{炉}{Q R} 鈮� \overset{炉}{S R}$ .

Step 3. Description of step.

Consider $螖 Q R O$ and $螖 S R O$ . From the given figure it can be observed that $\overset{炉}{R O} 鈮� \overset{炉}{R O}$ , $鈭� Q R O 鈮� 鈭� S R O$ and $\overset{炉}{Q R} 鈮� \overset{炉}{S R}$ then by SAS postulate, $螖 Q R O 鈮� 螖 S R O$ .

Step 4. Description of step.

As $螖 Q R O 鈮� 螖 S R O$ then by corresponding parts of congruent triangles, $\overset{炉}{Q O} 鈮� \overset{炉}{O S}$ which implies that O is the midpoint of $\overset{炉}{Q S}$ .

Step 5. Key steps of a proof.

Make a list of key steps of a proof.

$螖 P Q R 鈮� 螖 P S R$	HL postulate
$鈭� Q R P 鈮� 鈭� S R P$ ; $\overset{炉}{Q R} 鈮� \overset{炉}{S R}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 Q R O 鈮� 螖 S R O$	SAS postulate
O is the midpoint of $\overset{炉}{Q S}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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Short Answer

Step by step solution

Step 1. Description of step.

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

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).12. Given: PQ炉鈯�QR炉;PS炉鈯�SR炉;PQ炉鈮�PS炉Prove: O is the midpoint of QS炉.

Short Answer

Step by step solution

Step 1. Description of step.

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

Logic and Functions

Decision Maths

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.