Q23. Draw a four-sided figure ABCD聽w... [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 3: Q23. (page 82)

Draw a four-sided figure $A B C D$ with $\overset{炉}{A B} 鈭� \overset{炉}{D C}$ and $\overset{炉}{A D} 鈭� \overset{炉}{B C}$
Prove that $鈭� A 鈮� 鈭� C$
Is $鈭� B 鈮� 鈭� D$ ?

Short Answer

Expert verified

a. Proof is

Statement	Reason
1. $\overset{炉}{A B} 鈭� \overset{炉}{D C} and \overset{炉}{A D} 鈭� \overset{炉}{B C}$	Given
2. $鈭� A$ is supplementary to $鈭� B$	Same-side interior angles
3. $鈭� B$ is supplementary to $鈭� C$	Same-side interior angles
4. $鈭� A 鈮� 鈭� C$	If two angles are supplementary of same angle then both angles are congruent

b. Yes, $鈭� B 鈮� 鈭� D$

Step by step solution

Part a. Step 1. Draw required figure.

Part a. Step 2. Observe figure.

Line segment $\overset{炉}{A B}$ is transversal to parallel lines $\overset{炉}{A D}$ and $\overset{炉}{B C}$

Line segment $\overset{炉}{B C}$ is transversal to parallel lines $\overset{炉}{A B}$ and $\overset{炉}{D C}$

Part a. Step 3. Write two column proof to prove that ∠A≅∠C.

Statement	Reason
1. $\overset{炉}{A B} 鈭� \overset{炉}{D C} and \overset{炉}{A D} 鈭� \overset{炉}{B C}$	Given
2. $鈭� A$ is supplementary to $鈭� B$	Same-side interior angles
3. $鈭� B$ is supplementary to $鈭� C$	Same-side interior angles
4. $鈭� A 鈮� 鈭� C$	If two angles are supplementary of same angle then both angles are congruent

Hence $鈭� A 鈮� 鈭� C$ proved.

Part b. Step 1. First Observation from figure.

Line segment $\overset{炉}{A B}$ is transversal to parallel lines $\overset{炉}{A D}$ and $\overset{炉}{B C}$

Line segment $\overset{炉}{A D}$ is transversal to parallel lines $\overset{炉}{A B}$ and $\overset{炉}{D C}$

Part b. Step 2. Second observation from figure.

$鈭� A$ and $鈭� B$ forms a pair of same-side interior angles

$鈭� A$ and $鈭� D$ forms a pair of same-side interior angles

Part b. Step 3. Same-side interior angles.

Using theorem:. If two parallel lines are cut by a transversal line than the pairs of same side interior angles are supplementary.

$鈭� A$ is supplementary to $鈭� B$ and $鈭� A$ is supplementary to $鈭� D$

If two angles are supplementary of same angle then both angles are congruent

Hence, $鈭� B 鈮� 鈭� D$

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91影视

Draw a four-sided figure $A B C D$ with $\overset{炉}{A B} 鈭� \overset{炉}{D C}$ and $\overset{炉}{A D} 鈭� \overset{炉}{B C}$
Prove that $鈭� A 鈮� 鈭� C$
Is $鈭� B 鈮� 鈭� D$ ?

Short Answer

Step by step solution

Part a. Step 1. Draw required figure.

Part a. Step 2. Observe figure.

Part a. Step 3. Write two column proof to prove that ∠A≅∠C.

Part b. Step 1. First Observation from figure.

Part b. Step 2. Second observation from figure.

Part b. Step 3. Same-side interior angles.

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91影视

Draw a four-sided figure ABCDwith AB炉鈭�DC炉andAD炉鈭�BC炉Prove that鈭�A鈮�鈭�CIs 鈭�B鈮�鈭�D?

Short Answer

Step by step solution

Part a. Step 1. Draw required figure.

Part a. Step 2. Observe figure.

Part a. Step 3. Write two column proof to prove that ∠A≅∠C.

Part b. Step 1. First Observation from figure.

Part b. Step 2. Second observation from figure.

Part b. Step 3. Same-side interior angles.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Draw a four-sided figure $A B C D$ with $\overset{炉}{A B} 鈭� \overset{炉}{D C}$ and $\overset{炉}{A D} 鈭� \overset{炉}{B C}$
Prove that $鈭� A 鈮� 鈭� C$
Is $鈭� B 鈮� 鈭� D$ ?