Q6. In Exercises 1-6 you are given a... [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: Q6. (page 149)

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.
Prove: $鈭� CBA 鈮� 鈭� DBA$
Key steps of proof:
a. $\overset{炉}{OC} 鈮� \overset{炉}{OD}$
b. $螖 CAO 鈮� 螖 DAO$
c. $鈭� CAO 鈮� 鈭� DAO$
d. $螖 CAB 鈮� 螖 DAB$
e. $鈭� CBA 鈮� 鈭� DBA$

Short Answer

Expert verified

a. $\overset{炉}{O D} 鈮� \overset{炉}{O C}$	Converse of isosceles triangle theorem
b. $螖 C A O 鈮� 螖 D A O$	SSS postulate
c. $鈭� C A O 鈮� 鈭� D A O$	Corr. parts of $鈮� 螖$ are $鈮�$ .
d. $螖 C A B 鈮� 螖 D A B$	SAS postulate
e. $鈭� C B A 鈮� 鈭� D B A$	Corr. parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Description of step.

Consider $螖 C O D, 鈭� O C D 鈮� 鈭� O D C$ then by converse of an isosceles triangle theorem, that is, if the two angles of a triangle are congruent then sides opposite to those angles are congruent, $\overset{炉}{O D} 鈮� \overset{炉}{O C}$ .

Step 2. Apply SSS postulate.

Consider $螖 C A O$ and $螖 D A O$ in which $\overset{炉}{O D} 鈮� \overset{炉}{O C}, \overset{炉}{A C} 鈮� \overset{炉}{A D}$ and $\overset{炉}{O A} 鈮� \overset{炉}{O A}$ then by SSS postulate width="112" height="20" role="math">螖CAO鈮�螖DAO.

Step 3. Description of step.

As $螖 C A O 鈮� 螖 D A O$ , by corresponding parts of congruent triangles, $鈭� C A O 鈮� 鈭� D A O$ .

Step 4. Apply SAS postulate.

Consider $螖 C A B$ and $螖 D A B$ in which $\overset{炉}{A C} 鈮� \overset{炉}{A D}, \overset{炉}{A B} 鈮� \overset{炉}{A B}$ and $鈭� C A B 鈮� 鈭� D A B$ then by SAS postulate $螖 C A B 鈮� 螖 D A B$ .

Step 5. Description of step.

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

Step 6. Give the reason for each key step of the proof.

a. $\overset{炉}{O D} 鈮� \overset{炉}{O C}$	Converse of isosceles triangle theorem
b. $螖 C A O 鈮� 螖 D A O$	SSS postulate
c. $鈭� C A O 鈮� 鈭� D A O$	Corr. parts of $鈮� 螖$ are $鈮�$ .
d. $螖 C A B 鈮� 螖 D A B$	SAS postulate
e. $鈭� C B A 鈮� 鈭� D B A$	Corr. parts of $鈮� 螖$ are $鈮�$ .

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91影视

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Apply SSS postulate.

Step 3. Description of step.

Step 4. Apply SAS postulate.

Step 5. Description of step.

Step 6. Give the reason for each key step of the proof.

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91影视

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.Prove:鈭�CBA鈮�鈭�DBAKey steps of proof:a.OC炉鈮�OD炉b.螖CAO鈮�螖DAOc.鈭�CAO鈮�鈭�DAOd.螖CAB鈮�螖DABe.鈭�CBA鈮�鈭�DBA

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Apply SSS postulate.

Step 3. Description of step.

Step 4. Apply SAS postulate.

Step 5. Description of step.

Step 6. Give the reason for each key step of the proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Probability and Statistics

Geometry

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.