Q29 Given: 聽鈻盇BZY; 聽AY炉鈮匓X炉;... [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: Q29 (page 188)

Given: $鈻� ABZY$ ; $\overset{炉}{AY} 鈮� \overset{炉}{BX}$ ;
Prove: $鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$ .

Short Answer

Expert verified

$鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$

Step by step solution

Step 1. Consider the diagram.

Parallelogram ABZY is:

Here, $\overset{炉}{A Y} 鈮� \overset{炉}{B X}$ .

Step 2. State the proof.

In $螖 A Y Z$ and $螖 A B Z$ ,

Statement	Reason
$Z B 鈮� A B$	The sides of a rhombus are equal.
$鈭� 1 鈮� 鈭� 3$ 鈥︹€� (1)	Angles opposite to equal sides are equal.
$A Y 鈭� B Z$	The opposite sides of a rhombus are parallel and transversal $A Z$ .
$鈭� 1 鈮� 鈭� 4$ 鈥︹€� (2)	Alternate angles.

From (1) and (2),

$鈭� 2 鈮� 鈭� 1$

Thus, $鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$ .

Step 3. State the conclusion.

Therefore, $鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$ (proved).

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91影视

Given: $鈻� ABZY$ ; $\overset{炉}{AY} 鈮� \overset{炉}{BX}$ ;
Prove: $鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$ .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

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91影视

Given: 鈻�ABZY; AY炉鈮�BX炉;Prove: 鈭�1鈮�鈭�2and 鈭�1鈮�鈭�3.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Statistics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Given: $鈻� ABZY$ ; $\overset{炉}{AY} 鈮� \overset{炉}{BX}$ ;
Prove: $鈭� 1 鈮� 鈭� 2$ and $鈭� 1 鈮� 鈭� 3$ .