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: Q5. (page 146)

Given: $\overset{炉}{M B} 鈮� \overset{炉}{N C}; \overset{炉}{B N} 鈯� \overset{炉}{A C}; \overset{炉}{C M} 鈯� \overset{炉}{A B}$
Prove: $\overset{炉}{C M} 鈮� \overset{炉}{B N}$

Short Answer

Expert verified

Two column proof is

Statement	Reason
1. $m 鈭� C N B = m 鈭� B M C$	Each
2. $\overset{炉}{C B} 鈮� \overset{炉}{B C}$	Reflexive property
3. $\overset{炉}{M B} 鈮� \overset{炉}{N C}$	Given
4. $螖 C N B 鈮� 螖 B M C$	HL Theorem
5. $\overset{炉}{B N} 鈮� \overset{炉}{C M}$	Corresponding Parts of Congruent Triangle

Step by step solution

- Consider triangles ΔCNB and ΔBMC

As $m 鈭� B M C = 90 掳$ and $m 鈭� C N B = 90 掳$ , so both triangles are right angle triangle.

$\overset{炉}{B C}$ is hypotenuse in both triangles $螖 B M C and 螖 C N B$

- Use reflexive property

In triangles $螖 C N B and 螖 B M C$ , by using reflexive property common side of two triangle is congruent. So $\overset{炉}{C B} 鈮� \overset{炉}{B C}$

- Prove ΔCNB≅ΔBMC

As hypotenuse and one leg of both right angle triangle is congruent to each other.

Using $H L$ Theorem 鈥淚f the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.鈥�

Thus, $螖 C N B 鈮� 螖 B M C$

- Prove BN¯≅CM¯

As corresponding parts of congruent triangles are congruent so $\overset{炉}{B N} 鈮� \overset{炉}{C M}$

Thus, two column proof is

Statement	Reason
1. $m 鈭� C N B = m 鈭� B M C$	Each
2. $\overset{炉}{C B} 鈮� \overset{炉}{B C}$	Reflexive property
3. $\overset{炉}{M B} 鈮� \overset{炉}{N C}$	Given
4. $螖 C N B 鈮� 螖 B M C$	HL Theorem
5. $\overset{炉}{B N} 鈮� \overset{炉}{C M}$	Corresponding Parts of Congruent Triangle

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91影视

Given: $\overset{炉}{M B} 鈮� \overset{炉}{N C}; \overset{炉}{B N} 鈯� \overset{炉}{A C}; \overset{炉}{C M} 鈯� \overset{炉}{A B}$
Prove: $\overset{炉}{C M} 鈮� \overset{炉}{B N}$

Short Answer

Step by step solution

- Consider triangles ΔCNB and ΔBMC

- Use reflexive property

- Prove ΔCNB≅ΔBMC

- Prove BN¯≅CM¯

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91影视

Given:MB炉鈮�NC炉;BN炉鈯�AC炉;CM炉鈯�AB炉Prove:CM炉鈮�BN炉

Short Answer

Step by step solution

- Consider triangles ΔCNB and ΔBMC

- Use reflexive property

- Prove ΔCNB≅ΔBMC

- Prove BN¯≅CM¯

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Probability and Statistics

Geometry

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Given: $\overset{炉}{M B} 鈮� \overset{炉}{N C}; \overset{炉}{B N} 鈯� \overset{炉}{A C}; \overset{炉}{C M} 鈯� \overset{炉}{A B}$
Prove: $\overset{炉}{C M} 鈮� \overset{炉}{B N}$