Q33 Find something interesting to pr... [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 5: Q33 (page 171)

Find something interesting to prove. Then prove it. Answers may vary.
Given: $鈻� ABCD; 鈭� 1 鈮� 鈭� 2$

Short Answer

Expert verified

It is proved that $\overset{炉}{A X} 鈮� \overset{炉}{C Y}$ .

Step by step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

In $鈻� A B C D$ , $\overset{炉}{A D}$ and $\overset{炉}{B C}$ are opposite sides. Therefore, $\overset{炉}{A D} 鈮� \overset{炉}{B C}$ .

Step 2. Description of step.

From the given figure, it can be observed that $\overset{炉}{A D} 鈭� \overset{炉}{B C}$ and $\overset{炉}{A C}$ is a transversal then $鈭� D A C$ and $鈭� A C B$ are alternate interior angles such that, $鈭� D A C 鈮� 鈭� A C B$ .

Step 3. Description of step.

As $鈭� 1 鈮� 鈭� 2$ , $\overset{炉}{A D} 鈮� \overset{炉}{B C}$ and $鈭� D A C 鈮� 鈭� A C B$ then by ASA postulate, $螖 D A X 鈮� 螖 B C Y$ .

Step 4. Description of step.

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

Hence it is proved that $\overset{炉}{A X} 鈮� \overset{炉}{C Y}$ .

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91影视

Find something interesting to prove. Then prove it. Answers may vary.
Given: $鈻� ABCD; 鈭� 1 鈮� 鈭� 2$

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

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91影视

Find something interesting to prove. Then prove it. Answers may vary.Given: 鈻�ABCD;鈭�1鈮�鈭�2

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

Mechanics Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Find something interesting to prove. Then prove it. Answers may vary.
Given: $鈻� ABCD; 鈭� 1 鈮� 鈭� 2$