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Complete the proof....

Complete the proof....-example-1
User Debojyoti
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1 Answer

3 votes

Answer:

The correct options are;

1. Definition of supplementary angles

2. m∠1 + m∠2 = m∠1 + m∠3

3. m∠2 = m∠3

4. Definition of Congruent Angles

Explanation:

The two column proof is presented as follows;

Statement
{} Reason

1. ∠1 and ∠2 are supplementary
{} Given


{} ∠1 and ∠3 are supplementary

2. m∠1 + m∠2 = 180°
{} Definition of supplementary angles


{} m∠1 + m∠3 = 180°

3. m∠1 + m∠2 = m∠1 + m∠3
{} Transitive Property

4. m∠2 = m∠3
{} Subtraction Property of Equality

5. ∠2 ≅ ∠3
{} Definition of Congruent Angles

Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.

User SmasherHell
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