Q15. Given: AM炉鈮匨B炉;聽AD炉鈮匓C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 4: Q15. (page 151)

Given: $\overset{炉}{AM} 鈮� \overset{炉}{MB}; \overset{炉}{AD} 鈮� \overset{炉}{BC}$
$鈭� MDC 鈮� 鈭� MCD$
Prove: $\overset{炉}{AC} 鈮� \overset{炉}{BD}$

Short Answer

Expert verified

$螖 ADM 鈮� 螖 BCM$ by SSS postulate then by corresponding parts of congruent triangles $鈭� ADC 鈮� 鈭� BCD$ . $螖 ADC 鈮� 螖 BCD$ by SAS postulate then corresponding parts of congruent triangles, $\overset{炉}{AC} 鈮� \overset{炉}{BD}$ .

Step by step solution

Step 1. Description of step.

Consider $螖 A D M$ and $螖 B C M$ . From the given figure it can be observed that $\overset{炉}{A D} 鈮� \overset{炉}{B C}$ , $\overset{炉}{D M} 鈮� \overset{炉}{C M}$ and $\overset{炉}{A M} 鈮� \overset{炉}{M B}$ then by SSS postulate, $螖 A D M 鈮� 螖 B C M$ .

Step 2. Description of step.

As $螖 A D M 鈮� 螖 B C M$ then by corresponding parts of congruent triangles $鈭� A D M 鈮� 鈭� B C M$ and $鈭� M D C 鈮� 鈭� M C D$ which implies that $鈭� A D C 鈮� 鈭� B C D$ .

Step 3. Description of step.

Consider $螖 A D C$ and $螖 B C D$ . From the given figure it can be observed that $\overset{炉}{A D} 鈮� \overset{炉}{B C}$ , $鈭� A D C 鈮� 鈭� B C D$ and $\overset{炉}{C D} 鈮� \overset{炉}{C D}$ then by SAS postulate, $螖 A D C 鈮� 螖 B C D$ .

Step 4. Description of step.

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

Step 5. Write a paragraph proof.

$螖 A D M 鈮� 螖 B C M$ by SSS postulate then by corresponding parts of congruent triangles $鈭� A D C 鈮� 鈭� B C D$ . $螖 A D C 鈮� 螖 B C D$ by SAS postulate then corresponding parts of congruent triangles, $\overset{炉}{A C} 鈮� \overset{炉}{B D}$ .

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91影视

Given: $\overset{炉}{AM} 鈮� \overset{炉}{MB}; \overset{炉}{AD} 鈮� \overset{炉}{BC}$
$鈭� MDC 鈮� 鈭� MCD$
Prove: $\overset{炉}{AC} 鈮� \overset{炉}{BD}$

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

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91影视

Given: AM炉鈮�MB炉;AD炉鈮�BC炉鈭�MDC鈮�鈭�MCDProve: AC炉鈮�BD炉

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{AM} 鈮� \overset{炉}{MB}; \overset{炉}{AD} 鈮� \overset{炉}{BC}$
$鈭� MDC 鈮� 鈭� MCD$
Prove: $\overset{炉}{AC} 鈮� \overset{炉}{BD}$