Q3. In Exercises 1-3 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 148)

In Exercises 1-3 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.
Prove: $鈭� 3 鈮� 鈭� 4$
Key steps of proof:
a. width="109" height="20" role="math">螖LOB鈮�螖JOB
b. $鈭� 1 鈮� 鈭� 2$
c. $螖 LBA 鈮� 螖 JBA$
d. $鈭� 3 鈮� 鈭� 4$

Short Answer

Expert verified

a. $螖 L O B 鈮� 螖 J O B$	SSS postulate
b. $鈭� 1 鈮� 鈭� 2$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 L B A 鈮� 螖 J B A$	SAS postulate
d. $鈭� 3 鈮� 鈭� 4$	Corr. parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Apply SSS postulate.

Consider $螖 L O B$ and $螖 J O B$ in which $\overset{炉}{L O} 鈮� \overset{炉}{J O}, \overset{炉}{O B} 鈮� \overset{炉}{O B}$ and $\overset{炉}{L B} 鈮� \overset{炉}{J B}$ then by SSS postulate width="105">螖LOB鈮�螖JOB.

Step 2. Description of step.

As $螖 L O B 鈮� 螖 J O B$ , by corresponding parts of congruent triangles, width="68">鈭�1鈮�鈭�2.

Step 3. Apply SAS postulate.

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

Step 4. Description of step.

As $螖 L B A 鈮� 螖 J B A$ , by corresponding parts of congruent triangles, $鈭� 3 鈮� 鈭� 4$ .

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

a. $螖 L O B 鈮� 螖 J O B$	SSS postulate
b. $鈭� 1 鈮� 鈭� 2$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 L B A 鈮� 螖 J B A$	SAS postulate
d. $鈭� 3 鈮� 鈭� 4$	Corr. parts of $鈮� 螖$ are $鈮�$ .