Q3. 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: Q3. (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: $鈭� G 鈮� 鈭� T$
Key steps of proof:
a. $螖 RAJ 鈮� 螖 NAK$
b. $\overset{炉}{RJ} 鈮� \overset{炉}{NK}$
c. $螖 GRJ 鈮� 螖 TNK$
d. $鈭� G 鈮� 鈭� T$

Short Answer

Expert verified

a. $螖 R A J 鈮� 螖 N A K$	AAS postulate
b. $\overset{炉}{R J} 鈮� \overset{炉}{N K}$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 G R J 鈮� 螖 T N K$	SAS postulate
d. $鈭� G 鈮� 鈭� T$	Corr. parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Apply AAS postulate.

Consider $螖 R A J$ and $螖 N A K$ in which $\overset{炉}{R A} 鈮� \overset{炉}{N A}, 鈭� R A J 鈮� 鈭� N A K$ and $鈭� R J A 鈮� 鈭� N K A$ then by AAS postulate width="107">螖RAJ鈮�螖NAK.

Step 2. Description of step.

As $螖 R A J 鈮� 螖 N A K$ , by corresponding parts of congruent triangles, width="63">RJ炉鈮�NK炉.

Step 3. Apply SAS postulate.

Consider $螖 G R J$ and $螖 T N K$ in which $\overset{炉}{G J} 鈮� \overset{炉}{T K}, 鈭� G J R 鈮� 鈭� T K N$ and $\overset{炉}{R J} 鈮� \overset{炉}{N K}$ then by SAS postulate width="107">螖GRJ鈮�螖TNK.

Step 4. Description of step.

As $螖 G R J 鈮� 螖 T N K$ , by corresponding parts of congruent triangles, $鈭� G 鈮� 鈭� T$ .

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

a. $螖 R A J 鈮� 螖 N A K$	AAS postulate
b. $\overset{炉}{R J} 鈮� \overset{炉}{N K}$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 G R J 鈮� 螖 T N K$	SAS postulate
d. $鈭� G 鈮� 鈭� T$	Corr. parts of $鈮� 螖$ are $鈮�$ .

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91影视

Short Answer

Step by step solution

Step 1. Apply AAS postulate.

Step 2. Description of step.

Step 3. Apply SAS 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: 鈭�G鈮�鈭�TKey steps of proof:a.螖RAJ鈮�螖NAKb.RJ炉鈮�NK炉c.螖GRJ鈮�螖TNKd.鈭�G鈮�鈭�T

Short Answer

Step by step solution

Step 1. Apply AAS postulate.

Step 2. Description of step.

Step 3. Apply SAS 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

Applied Mathematics

Pure Maths

Decision Maths

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.