Given: Angle 1 and angle 2 are supplementary. Angle 3 and angle 4 are supplementary. Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4.

Question

This is supposed to be a two column proof. It has statements on one side and reasons on the other. the first three statements are: Angle 1 and angle 2 are supplementary
Angle 3 and angle 4 are supplementary
Angle 1 is congruent to angle 3

 

Given: Angle 1 and angle 2 are supplementary.
Angle 3 and angle 4 are supplementary.
Angle 1 is congruent to angle 3.
Prove: Angle 2 is congruent to angle 4.

Answer 1

Hi Inga,

 

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