Q11. 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: Q11. (page 150)

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps).
Given: $\overset{炉}{DE} 鈮� \overset{炉}{FG}; \overset{炉}{GD} 鈮� \overset{炉}{EF}$ ;
$鈭� HDE and 鈭� KFG are rt . 鈭� s$
Prove: $\overset{炉}{DH} 鈮� \overset{炉}{FK}$

Short Answer

Expert verified

$螖 GDE 鈮� 螖 EFG$	SSS postulate
$鈭� DEG 鈮� 鈭� FGE$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 HDE 鈮� 螖 KFG$	ASA postulate
$\overset{炉}{DH} 鈮� \overset{炉}{FK}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Description of step.

Consider $螖 G D E$ and $螖 E F G$ . From the given figure it can be observed that $\overset{炉}{D E} 鈮� \overset{炉}{F G}, \overset{炉}{G D} 鈮� \overset{炉}{E F}$ and $\overset{炉}{E G} 鈮� \overset{炉}{E G}$ then by SSS postulate, $螖 G D E 鈮� 螖 E F G$ .

Step 2. Description of step.

As $螖 G D E 鈮� 螖 E F G$ then by corresponding parts of congruent triangles, $鈭� D E G 鈮� 鈭� F G E$ .

Step 3. Description of step.

Consider $螖 H D E$ and $螖 K F G$ . From the given figure it can be observed that $\overset{炉}{D E} 鈮� \overset{炉}{F G}$ , $鈭� H D E 鈮� 鈭� K F G$ and $鈭� D E H 鈮� 鈭� F G K$ then by ASA postulate, $螖 H D E 鈮� 螖 K F G$ .

Step 4. Description of step.

As $螖 H D E 鈮� 螖 K F G$ then by corresponding parts of congruent triangles, $\overset{炉}{D H} 鈮� \overset{炉}{F K}$ .

Step 5. Key steps of a proof.

Make a list of key steps of a proof.

$螖 G D E 鈮� 螖 E F G$	SSS postulate
$鈭� D E G 鈮� 鈭� F G E$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 H D E 鈮� 螖 K F G$	ASA postulate
$\overset{炉}{D H} 鈮� \overset{炉}{F K}$	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).Given: DE炉鈮�FG炉;GD炉鈮�EF炉;鈭�HDEand鈭�KFGarert.鈭�sProve: DH炉鈮�FK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

Decision Maths

Calculus

Pure Maths

Discrete Mathematics

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.