Complete the following proof. You may use an answer more than once.
Given: <1 and <2 are complementary; <1 = <4
Prove: <3 and <4 are complementary
1: <1 and <2 are complementary/ Given
2: m<1 +m<2= 90/
3: <1=<4/Given
4: m<1 = m<4/ Definition of congruence
5: <2=<3/
6: m<2=m<3/ Definition of congruence
7: m<4 + m<3=90/
Choices are
Definition of Supplementary angles
Definition of linear pair
Substitution
Vertical Angle Therorem
Definition of complementary angles
Given
The proof can be completed using the steps as follows:
1: <1 and <2 are complementary/ Given
2: m<1 +m<2 = 90/ Definition of complementary angles
3: <1 = <4/ Given
4: m<1 = m<4/ Definition of congruence
5: <2 = <3/ Substitution (using step 3)
6: m<2 = m<3/ Definition of congruence
7: m<4 + m<3 = 90/ Definition of supplementary angles
Therefore, by definition of supplementary angles, <3 and <4 are complementary.
To complete the proof, we can use the following steps:
1: <1 and <2 are complementary/ Given.
2: m<1 +m<2 = 90/ Definition of complementary angles.
3: <1 = <4/ Given.
4: m<1 = m<4/ Definition of congruence.
5: <2 = <3/ Substitution (using step 3 and 4).
6: m<2 = m<3/ Definition of congruence.
7: m<4 + m<3 = 90/ Definition of complementary angles.
From the steps above, we can see that <3 and <4 have the same measures as <2 and <1, respectively. Since <1 and <2 are complementary, their measures add up to 90 degrees. Therefore, by substitution, we can conclude that <3 and <4 are also complementary.
Therefore, the proof can be completed using the choice "Substitution."
To complete the proof, you can use the following steps:
1: <1 and <2 are complementary/ Given
2: m<1 + m<2 = 90/ Definition of Complementary angles
3: <1 = <4/ Given
4: m<1 = m<4/ Definition of Congruence
5: <2 = <3/
6: m<2 = m<3/ Definition of Congruence
7: m<4 + m<3 = 90/ (This is the step you need to complete)
To complete step 7, you can use the "Substitution" property. Since you know that <1 = <4, you can substitute <4 in place of <1 in step 2.
So, step 7 should be: m<4 + m<3 = 90/ Substitution
By using the "Substitution" property, you have shown that <3 and <4 are complementary angles.