Q4. Write proofs in two鈥揷olumn for... [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: Q4. (page 130)

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{A B}$ ; $鈭� 1 鈮� 鈭� 2; 鈭� 3 鈮� 鈭� 4$
Prove: $\overset{炉}{A C} 鈮� \overset{炉}{B D}$

Short Answer

Expert verified

Two column proof is

Statement	Reason
1. $鈭� 1 鈮� 鈭� 2$	Given
2. $\overset{炉}{A M} 鈮� \overset{炉}{B M}$	Definition of midpoint
3. $鈭� 3 鈮� 鈭� 4$	Given
4. $螖 W O X 鈮� 螖 ZOY$	ASA congruency criteria
5. $\overset{炉}{A C} 鈮� \overset{炉}{B D}$	corresponding parts of congruent triangle are congruent

Step by step solution

Step 1. Show that AM¯≅BM¯.

By definition of midpoint

$\overset{炉}{A M} 鈮� \overset{炉}{B M}$

Step 2. Show ΔACM≅ΔBDM.

Using step 1 and given statement $螖 A C M 鈮� 螖 B D M$ by ASA (Angle-Side-Angle) congruency criteria

Step 3. Show AC¯≅BD¯.

Since, corresponding parts of congruent triangle are congruent

So, $\overset{炉}{A C} 鈮� \overset{炉}{B D}$

Thus, two column proof is

Statement	Reason
1. $鈭� 1 鈮� 鈭� 2$	Given
2. $\overset{炉}{A M} 鈮� \overset{炉}{B M}$	Definition of midpoint
3. $鈭� 3 鈮� 鈭� 4$	Given
4. $螖 W O X 鈮� 螖 ZOY$	ASA congruency criteria
5. $\overset{炉}{A C} 鈮� \overset{炉}{B D}$	corresponding parts of congruent triangle are congruent

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91影视

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{A B}$ ; $鈭� 1 鈮� 鈭� 2; 鈭� 3 鈮� 鈭� 4$
Prove: $\overset{炉}{A C} 鈮� \overset{炉}{B D}$

Short Answer

Step by step solution

Step 1. Show that AM¯≅BM¯.

Step 2. Show ΔACM≅ΔBDM.

Step 3. Show AC¯≅BD¯.

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91影视

Write proofs in two鈥揷olumn form.Given: Mis the midpoint of AB炉;鈭�1鈮�鈭�2;鈭�3鈮�鈭�4Prove: AC炉鈮�BD炉

Short Answer

Step by step solution

Step 1. Show that AM¯≅BM¯.

Step 2. Show ΔACM≅ΔBDM.

Step 3. Show AC¯≅BD¯.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write proofs in two鈥揷olumn form.
Given: $M$ is the midpoint of $\overset{炉}{A B}$ ; $鈭� 1 鈮� 鈭� 2; 鈭� 3 鈮� 鈭� 4$
Prove: $\overset{炉}{A C} 鈮� \overset{炉}{B D}$