Question

Complete the paragraph proof.

Answer 1

Answer:

(a) 180°

(b) 180°

(c) substitution property

(d) m∠3

(e) ∠3

Step-by-step explanation:

Definition: Two angles are supplementary if they add up to 180°

Proof:

By definition of supplementary angles, m∠1 + m∠2 = 180° (a) {∠1 and ∠2 are supplementary - given}

and  m∠2 + m∠3 = 180° (b) {∠2 and ∠3 are supplementary - given}

Then, m∠1 + m∠2 = m∠2 + m∠3 by the substitution property (c)

Subtract m∠2 from each side. You get m∠1 = m∠3 (d)

or ∠1 ≅ ∠3 (e)

Answer 2

Answer:

(a) 180°

(b) 180°

(c) transitive property of equality

(d) m∠3

(e) ∠3

Step-by-step explanation:

Given : ∠1 and ∠2 are supplementary and ∠2 and ∠3 are supplementary,

Prove : ∠1 ≅ ∠3 ,

By the definition of supplementary angles,

m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°,

Then,  m∠1 + m∠2 = m∠2 + m∠3 by the transitive property of equality,

Subtract m∠2 from each sides,

m∠1 = m∠3,

or ∠1 ≅ ∠3

Hence, proved....