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2 years ago

Unit 3 parallel and perpendicular lines homework 4 parallel line proofs

Mathematics

1 answer:

Alex17521 [72]2 years ago

6 0

Answer:

1) c ║ d by consecutive interior angles theorem

2) m∠3 + m∠6 = 180° by transitive property

3) ∠2 ≅ ∠5 by definition of congruency

4) t ║ v ${}$ Corresponding angle theorem

5) ∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

6) ∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem

Step-by-step explanation:

1) Statement ${}$ Reason

m∠4 + m∠7 = 180° ${}$ Given

m∠4 ≅ m∠6 ${}$ Vertically opposite angles

m∠4 = m∠6 ${}$ Definition of congruency

m∠6 + m∠7 = 180° ${}$ Transitive property

m∠6 and m∠7 are supplementary ${}$ Definition of supplementary angles

∴ c ║ d ${}$ Consecutive interior angles theorem

2) Statement ${}$ Reason

m∠3 = m∠8 ${}$ Given

m∠8 + m∠6 = 180° ${}$ Sum of angles on a straight line

∴ m∠3 + m∠6 = 180° ${}$ Transitive property

3) Statement ${}$ Reason

p ║ q ${}$ Given

∠1 ≅ ∠5 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

∠2 ≅ ∠1 ${}$ Alternate interior angles theorem

∠2 = ∠1 ${}$ Definition of congruency

∠2 = ∠5 ${}$ Transitive property

∠2 ≅ ∠5 ${}$ Definition of congruency.

4) Statement ${}$ Reason

∠1 ≅ ∠5 ${}$ Given

∠3 ≅ ∠4 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

∠3 = ∠4 ${}$ Definition of congruency

∠5 ≅ ∠4 ${}$ Vertically opposite angles

∠5 = ∠4 ${}$ Definition of congruency

∠5 = ∠3 ${}$ Transitive property

∠1 = ∠3 ${}$ Transitive property

∠1 ≅ ∠3 ${}$ Definition of congruency.

t ║ v ${}$ Corresponding angle theorem

5) Statement ${}$ Reason

∠5 ≅ ∠16 ${}$ Given

∠2 ≅ ∠4 ${}$ Given

∠5 = ∠16 ${}$ Definition of congruency

∠2 = ∠4 ${}$ Definition of congruency

EF ║ GH ${}$ Corresponding angle theorem

∠14 ≅ ∠16 ${}$ Corresponding angles

∠14 = ∠16 ${}$ Definition of congruency

∠5 = ∠14 ${}$ Transitive property

∠5 + ∠11 = 180° ${}$ Sum of angles on a straight line

∠14 + ∠11 = 180° ${}$ Transitive property

∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

6) Statement ${}$ Reason

l ║ m ${}$ Given

∠4 ≅ ∠7 ${}$ Given

∠4 = ∠7 ${}$ Definition of congruency

∠2 ≅ ∠7 ${}$ Alternate angles

∠2 = ∠7 ${}$ Definition of congruency

∠2 = ∠4 ${}$ Transitive property

∠2 ≅ ∠4 ${}$ Definition of congruency

∠2 and ∠4 are corresponding angles ${}$ Definition

DA ║ EB ${}$ Corresponding angle theorem

∠8 and ∠9 are consecutive interior angles ${}$ Definition

∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem.

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