Question

LO I OV by What's More Activity 2: "Form a Proof Write direct proof in paragraph form. Given: 21 23 21 and 22 are supplementary angles 23 and 24 are supplementary angles Prove: 2224 2 3 4​

Answer 1

Step-by-step explanation:

This proof involves the definitions of congruence and supplementary angles, as well as some of the properties of equality.

∠1 and ∠2 are supplementary // given

∠3 and ∠4 are supplementary // given

∠1 ≅ ∠3 // given

m∠1 + m∠2 = 180° // definition of supplementary angles

m∠3 + m∠4 = 180° // definition of supplementary angles

m∠1 + m∠2 = m∠3 + m∠4 // transitive property of equality

m∠1 = m∠3 // definition of congruent angles

m∠1 + m∠2 = m∠1 + m∠4 // substitution property of equality (replaced m∠3 with m∠1)

m∠2 = m∠4 // subtraction property of equality (subtracted m∠1 from both sides)

∠2 ≅ ∠4 // definition of congruent angles