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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.6, Problem 12E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercise 11 and 12, provide the missing statements and reasons.

Given: ∠ 1 ≅ ∠ 2 ; ∠ 3 ≅ ∠ 4
∠ s 2 and 3 are complementary
Prove: ∠ s 1 and 4 are complementary
PROOF
Statements Reasons
1. ∠ 1 ≅ ∠ 3 and ∠ 3 ≅ ∠ 4 1. ?
2. ? and ? 2. If two ∠ s are ≅ , then their measures are equal.
3. ∠ s 2 and 3 are complementary
 3. ?
4. ? 4. The sum of the measures of complementary ∠ s is 90
5. m ∠ 1 + m ∠ 4 = 90 5. ?
6. ? 6. If the sum of the measures of two angles is 90 , then the angles are complementary

Chapter 1.6, Problem 12E, In Exercise 11 and 12, provide the missing statements and reasons. Given: 12;34 s 2 and 3 are

To determine

To find:

The missing statements and reasons.

Explanation

Given:

∠1≅∠2

∠3≅∠4

∠s 2 and 3 are complementary

The given figure is,

Figure (1)

And,

The given table is shown below.

PROOF
Statements Reasons
1. ∠1≅∠2 and ∠3≅∠4 1. ?
2. ? and ? 2. If two ∠s are ≅, then their measures are equal.
3. ∠s 2 and 3 are complementary
 3. ?
4. ? 4. The sum of the measures of complementary ∠s is 90
5. m∠1+m∠4=90 5. ?
6. ? 6. If the sum of the measures of two angles is 90, then the angles are complementary

Approach:

1. The perpendicular lines are two lines that meet to form congruent adjacent angles.

2. If two lines are perpendicular, then they meet to form right angles.

3. If two angles are congruent, their measures are equal.

4. The symmetric property for the congruence of angles is satisfied, If ∠1≅∠2, then ∠2≅∠1.

5. If the sum of the measures of two angles is 90, then the angles are complementary.

Calculation:

The reason for the first statement of the proof is “Given”, so the first statement is given as,

∠1≅∠2

And,

∠3≅∠4

The reason for the second statement of the proof is, “If two ∠s are ≅, then their measures are equal”. So, use this property in above equations.

m∠1≅m∠2

And,

m∠3≅m∠4

So, the second statements is,

m∠1≅m∠2

And,

m∠3≅m∠4

The reason for the third statement of the proof is “Given”. So, the statement is ∠s 2 and 3 are complementary

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