Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who completed the proof incorrectly? Explain.

line AB intersecting line GH at K

Angie's Proof

Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. m∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Definition of Supplementary Angles

3. m∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. m∠AKG = m∠HKB 4. Subtraction Property

Becky's Proof

Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. m∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Angle Addition Postulate

3. m∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. m∠AKG = m∠HKB 4. Subtraction Property

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

50

step-by-step explanation:

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