Q2. 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: Q2. (page 148)

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: $\overset{炉}{BE} 鈮� \overset{炉}{DF}$
Key steps of proof:
a. width="112" height="20" role="math">螖ABC鈮�螖CDA
b. $鈭� 1 鈮� 鈭� 2$
c. $螖 ABE 鈮� 螖 CDF$
d. $\overset{炉}{BE} 鈮� \overset{炉}{DF}$

Short Answer

Expert verified

a. $螖 A B C 鈮� 螖 C D A$	SSS postulate
b. $鈭� 1 鈮� 鈭� 2$	Corr. parts ofwidth="33" height="20" role="math">鈮�螖 are $鈮�$ .
c. $螖 A B E 鈮� 螖 C D F$	AAS postulate
d. $\overset{炉}{B E} 鈮� \overset{炉}{D F}$	Corr. parts of $鈮� 螖$ are $鈮�$ .

Step by step solution

Step 1. Apply SSS postulate.

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

Step 2. Description of step.

As $螖 A B C 鈮� 螖 C D A$ , by corresponding parts of congruent triangles, $鈭� 1 鈮� 鈭� 2$ .

Step 3. Apply AAS postulate.

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

Step 4. Description of step.

As $螖 A B E 鈮� 螖 C D F$ , by corresponding parts of congruent triangles, width="64">BE炉鈮�DF炉.

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

a. $螖 A B C 鈮� 螖 C D A$	SSS postulate
b. $鈭� 1 鈮� 鈭� 2$	Corr. parts of $鈮� 螖$ are $鈮�$ .
c. $螖 A B E 鈮� 螖 C D F$	AAS postulate
d. $\overset{炉}{B E} 鈮� \overset{炉}{D F}$	Corr. parts of $鈮� 螖$ are $鈮�$ .

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91影视

Short Answer

Step by step solution

Step 1. Apply SSS postulate.

Step 2. Description of step.

Step 3. Apply AAS 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:BE炉鈮�DF炉Key steps of proof:a. width="112" height="20" role="math">螖ABC鈮�螖CDAb.鈭�1鈮�鈭�2c.螖ABE鈮�螖CDFd.BE炉鈮�DF炉

Short Answer

Step by step solution

Step 1. Apply SSS postulate.

Step 2. Description of step.

Step 3. Apply AAS 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

Logic and Functions

Decision Maths

Statistics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.