Question

Match the following reasons with the statements in the given proof. Prove that if two angles are complementary to the same angle then they are equal in measure. 1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.
a) Substitution
2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90
b) Definition of complementary
3. m∠1 + m∠2 = m∠3 + m∠2
c) Subtraction property of equality
4. m∠1 = m∠3
d) Given

Answer 1

1. --> d

2. --> b

3. --> a

4. --> c

1 is d because that is the only piece of information that sounds like a given.

2 is b because we know that from the given, m∠1 is complementary to m∠2 and in the first problem, m∠1 + m∠2 = 90, they are added together. The definition of complementary angles is "Two angles with measures that, when added together, equal 90 degrees". Same thing with m∠3 and m∠2.

3 is a because since both of the problems equal 90 degrees, you can just take away the 90 and put an equal sign in between the two problems because they equal the same thing.

4 is c because you are subtracting m∠2 from the problems and ending up with just m∠1 = m∠3.

Hope this helps! :)

Answer 2

Answer:

1.   ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.-->Given(A)

2.   m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90-->Definition of complementary(D)

3.   m∠1 + m∠2 = m∠3 + m∠2-->Substitution(C)

4.   m∠1 = m∠3-->Subtraction property of equality(B)

Step-by-step explanation: