Q10. 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: Q10. (page 150)

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps)
Given: Congruent parts as marked in the diagram. Prove: $鈭� B 鈮� 鈭� F$
(Hint: First draw two auxiliary lines.)

Short Answer

Expert verified

$螖 ACD 鈮� 螖 AED$	SAS postulate
$\overset{炉}{AC} 鈮� \overset{炉}{AE}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 ABC 鈮� 螖 AFE$	SSS postulate
$鈭� B 鈮� 鈭� F$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Draw two auxiliary lines.

Step 2. Description of step.

Consider $螖 A C D$ and $螖 A E D$ . From the given figure it can be observed that $\overset{炉}{C D} 鈮� \overset{炉}{E D}, \overset{炉}{A D} 鈮� \overset{炉}{A D}$ and $鈭� C D A 鈮� 鈭� E D A$ then by SAS postulate, $螖 A C D 鈮� 螖 A E D$ .

Step 3. Description of step.

As $螖 A C D 鈮� 螖 A E D$ then by corresponding parts of congruent triangles, $\overset{炉}{A C} 鈮� \overset{炉}{A E}$ .

Step 4. Description of step.

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

Step 5. Description of step.

As $螖 A B C 鈮� 螖 A F E$ then by corresponding parts of congruent triangles, $鈭� B 鈮� 鈭� F$ .

Step 6. Key steps of a proof.

Make a list of key steps of a proof.

$螖 A C D 鈮� 螖 A E D$	SAS postulate
$\overset{炉}{A C} 鈮� \overset{炉}{A E}$	Corr. Parts of $鈮� 螖$ are $鈮�$ .
$螖 A B C 鈮� 螖 A F E$	SSS postulate
$鈭� B 鈮� 鈭� F$	Corr. Parts of $鈮� 螖$ are $鈮�$ .

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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: Congruent parts as marked in the diagram. Prove: $鈭� B 鈮� 鈭� F$
(Hint: First draw two auxiliary lines.)

Short Answer

Step by step solution

Step 1. Draw two auxiliary lines.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

Step 6. 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: Congruent parts as marked in the diagram. Prove:鈭�B鈮�鈭�F(Hint: First draw two auxiliary lines.)

Short Answer

Step by step solution

Step 1. Draw two auxiliary lines.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

Step 6. Key steps of a proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Statistics

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Write proofs in the form specified by your teacher (two-column form, paragraph form, or a list of key steps)
Given: Congruent parts as marked in the diagram. Prove: $鈭� B 鈮� 鈭� F$
(Hint: First draw two auxiliary lines.)