Prove the second case of the Congruent Supplements Theorem where two angles are supplementary to congruent angles.

Given: <1 and <2 are supplements

<3 and <4 are supplements

<1 congruent <4

Prove: <2 congruent <3

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are given that angle 1 and angle 2 are supplements, angle 3 and angle 4 are supplements, and angle 1 is congruent to angle 4.

We are asked to prove that angle 2 is congruent to angle 3.

`/_1 "supplement"/_2`              Given

`m/_1+m/_2=180`                 Definition of supp. angles

`/_3"supplement" /_4`              Given

`m/_3+m/_4=180`                  Definition of supp angles

`m/_1+m/_2=m/_3+m/_4` Substitution

`/_1 cong /_4`                                     Given

`m/_1=m/_4`                             Definition of congruent

`m/_2=m/_3`                      Subtraction property of equality

`/_2 cong /_3`                            Definition of congruent

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial