Q4. 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: Q4. (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: $\overset{炉}{AL} 鈮� \overset{炉}{CM}$
Key steps of proof:
a. $螖 ABD 鈮� 螖 CDB$
b. $\overset{炉}{AD} 鈮� \overset{炉}{CB}; 鈭� 1 鈮� 鈭� 2$
c. $螖 ADL 鈮� 螖 CBM$
d. $\overset{炉}{AL} 鈮� \overset{炉}{CM}$

Short Answer

Expert verified

a. $螖 A B D 鈮� 螖 C D B$	SAS postulate
b. $\overset{炉}{A D} 鈮� \overset{炉}{C B}; 鈭� 1 鈮� 鈭� 2$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 A D L 鈮� 螖 C B M$	ASA postulate
d. $\overset{炉}{A L} 鈮� \overset{炉}{C M}$	Corr. parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Apply SAS postulate.

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

Step 2. Description of step.

As $螖 A B D 鈮� 螖 C D B$ , by corresponding parts of congruent triangles, $\overset{炉}{A D} 鈮� \overset{炉}{C B}; 鈭� 1 鈮� 鈭� 2$ .

Step 3. Apply ASA postulate.

Consider $螖 A D L$ and $螖 C B M$ in which $\overset{炉}{A D} 鈮� \overset{炉}{B C}, 鈭� 1 鈮� 鈭� 2$ and $鈭� D A L 鈮� 鈭� B C M$ then by ASA postulate $螖 A D L 鈮� 螖 C B M$ .

Step 4. Description of step.

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

Step 5. Give the reason for each key step of the proof.

a. $螖 A B D 鈮� 螖 C D B$	SAS postulate
b. $\overset{炉}{A D} 鈮� \overset{炉}{C B}; 鈭� 1 鈮� 鈭� 2$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 A D L 鈮� 螖 C B M$	ASA postulate
d. $\overset{炉}{A L} 鈮� \overset{炉}{C M}$	Corr. parts of $鈮� 螖$ are $鈮�$ .

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91影视

Short Answer

Step by step solution

Step 1. Apply SAS postulate.

Step 2. Description of step.

Step 3. Apply ASA postulate.

Step 4. Description of step.

Step 5. 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:AL炉鈮�CM炉Key steps of proof:a.螖ABD鈮�螖CDBb. AD炉鈮�CB炉;鈭�1鈮�鈭�2c.螖ADL鈮�螖CBMd.AL炉鈮�CM炉

Short Answer

Step by step solution

Step 1. Apply SAS postulate.

Step 2. Description of step.

Step 3. Apply ASA postulate.

Step 4. Description of step.

Step 5. 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

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.