Question

(30 pnts)Given: Lines y and z are parallel, and ABC forms a triangle.

Prove: m∠5 + m∠2 + m∠6 = 180°




Statements

Reasons
1. ABC is a triangle 1. given
2. y ∥ z 2. given
3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ?
4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅
5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate
6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle
7. m∠5 + m∠2 + m∠6 = 180° 7. substitution
Which could be the missing reason in Step 3?

alternate interior angles are congruent
alternate exterior angles are congruent
vertical angles are congruent
corresponding angles are congruent

Answer 1

Given : Lines y and z are parallel, and ABC forms a triangle.

Prove: m∠5 + m∠2 + m∠6 = 180°

Statements

Reasons

1. ABC is a triangle 1. given

2. y ∥ z 2. given

3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ?

4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅

5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate

6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle

7. m∠5 + m∠2 + m∠6 = 180° 7. substitution

To Find : Which could be the missing reason in Step 3?

alternate interior angles are congruent

alternate exterior angles are congruent

vertical angles are congruent

corresponding angles are congruent

Solution:

1. ABC is a triangle 1. given

2. y ∥ z 2. given

3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3.      Alternate interior angles

4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅

5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate

6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle

7. m∠5 + m∠2 + m∠6 = 180° 7. substitution

alternate interior angles are congruent is correct option,

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Answer 2

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Alternate interior Angles.