Question

Given: m<1=24 degrees, m<3=24 degrees, <1 and <2 are complementary, <3 and <4 are complementary Prove: <2 congruent <4

Answer 1

Do you need a two-column proof?

Answer 2

yeah
its a seven step proof

Answer 3

How do you know the number of steps?

Answer 4

We were given the number of steps

Answer 5

Ok.
This problem deals with complementary angles.
Do you know what complementary angles are?

Answer 6

yes angles that add up to 90 degrees

Answer 7

Great.
The first step in writing a proof is to figure out the entire problem. Then you can write it all out.

Answer 8

We are told this.
Angles 1 and 3 both measure 24 degrees. They are congruent.
Angle 1 is complementary to angle 2.
Angle 3 is complementary to angle 4.

Answer 9

Angles 2 and 4 are complementary to two congruent angles.
That means angles 2 and 4 must congruent to each other.

Answer 10

That is the reasoning behind this proof. Now we can actually write the proof.

Answer 11

Do you usually write all the given in one statement?

Answer 12

well in this problem i do not believe it is needed to split the given

Answer 13

Right. We can have all the given as one statement at the beginning.

Statements Reasons
1. m<1=24 degrees 1. Given
m<3=24 degrees
<1 and <2 are complementary
<3 and <4 are complementary
2. m<1 + m<2 = 90 2. Definition of complementary angles
3. m<3 + m<4 = 90 2. Definition of complementary angles

Answer 14

4. 24 + m<2 = 90 4. Substitution property of equality
5. 24 + m<4 = 90 5. Substitution property of equality
6. m<2 = 66 6. Subtraction property of equality
7. m<4 = 66 7. Subtraction property of equality
8. m<2 = m<4 8. Transitive property of equality

Answer 15

9. <2 is congruent to <4 9. Definition of congruent angles.