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: Q12. (page 131)

Given: $\overset{炉}{W X} 鈯� \overset{炉}{U V}; \overset{炉}{W X} 鈯� \overset{炉}{Y Z}; \overset{炉}{W U} 鈮� \overset{炉}{W V}$
Prove whatever you can about angles 1,2,3, and 4

Short Answer

Expert verified

Statements which can be proved are $鈭� 1 鈮� 鈭� 2$ and $鈭� 3 鈮� 鈭� 4$

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

By reflexive property of congruence,a side is congruent to itself

So, $\overset{炉}{W X} 鈮� \overset{炉}{W X}$

Also using given $m 鈭� 5 = m 鈭� 6 = 90 掳$

Thus, $螖 U W X 鈮� 螖 V W X$ by SAS (Side-Angle-Side) congruency criteria

Step 2. Show that ∠3≅∠4.

Since, corresponding parts of congruent triangles are congruent

So, $鈭� 3 鈮� 鈭� 4$

Step 3. Show that ∠1≅∠2.

Using given statement

$m 鈭� W X Y = m 鈭� W X Z = 90 掳$

Thus, $鈭� 1 + 鈭� 3 鈮� 鈭� 2 + 鈭� 4$

Substitute $鈭� 3$ for $鈭� 4$ in this equation

$\begin{matrix} 鈭� 1 + 鈭� 3 鈮� 鈭� 2 + 鈭� 3 \\ 鈭� 1 鈮� 鈭� 2 \end{matrix}$

Thus, statements which can be proved are $鈭� 1 鈮� 鈭� 2$ and $鈭� 3 鈮� 鈭� 4$

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91影视

Given: $\overset{炉}{W X} 鈯� \overset{炉}{U V}; \overset{炉}{W X} 鈯� \overset{炉}{Y Z}; \overset{炉}{W U} 鈮� \overset{炉}{W V}$
Prove whatever you can about angles 1,2,3, and 4

Short Answer

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

Step 2. Show that ∠3≅∠4.

Step 3. Show that ∠1≅∠2.

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91影视

Given:WX炉鈯�UV炉;WX炉鈯�YZ炉;WU炉鈮�WV炉Prove whatever you can about angles 1,2,3, and 4

Short Answer

Step by step solution

Step 1. Show that ΔUWX≅ΔVWX.

Step 2. Show that ∠3≅∠4.

Step 3. Show that ∠1≅∠2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Mechanics Maths

Statistics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{W X} 鈯� \overset{炉}{U V}; \overset{炉}{W X} 鈯� \overset{炉}{Y Z}; \overset{炉}{W U} 鈮� \overset{炉}{W V}$
Prove whatever you can about angles 1,2,3, and 4