Question

Geometry: Complete these proofs, ASAP!!!

Answer 1

The complete proofs are:

Proof 1

• a || b; c || d ⇒ Given
• ∠5 is supplementary to ∠4 ⇒ ∠5 + ∠4 = 180
• ∠2 = ∠4 ⇒ Definition of corresponding angles
• ∠5 + ∠2 = 180 ⇒ Substituting property of equality
• ∠5 + ∠2 = 180 ⇒ Definition of supplementary angles

Proof 2

• BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given
• ∠3 ≅ ∠4 ⇒ Definition of congruent angles
• ∠1 ≅ ∠3 ⇒ Definition of corresponding angles
• ∠1 ≅ ∠4 ⇒ Definition of corresponding angles

How to complete the proofs?

Proof 1

Lines a & b and c and d are given as parallel lines.

So, we have

a || b; c || d ⇒ Given

From the question, we have:

∠5 is supplementary to ∠4

So, we have

∠5 + ∠4 = 180

This is so because supplementary angles add up to 180

Corresponding angles are equal.

So, we have:

∠2 = ∠4

By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have

∠5 + ∠2 = 180

Hence, angles ∠5 and ∠2 are supplementary angles

Proof 2

Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.

So, we have

BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given

From the question, we have:

∠3 ≅ ∠4 ⇒ Definition of congruent angles

∠1 ≅ ∠3 ⇒ Definition of corresponding angles

Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4

∠1 ≅ ∠4

Hence, the angles 1 and 4 are congruent

Read more about supplementary angles at:

brainly.com/question/2046046

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