Give the reason for the step taken from a proof.
<1 is the supplement of <2---->Given
<3 is the supplement of <4---->Given
<2 = <4----------------------->Given
<1 = <3----------------------->?
a. linear pair postulate
b. congruent supplements theorem
c. congruent complements theorem
d. vertical angles theorem
when i use the = sign it it supposed to be the "is congruent to" sign. Just add a squiggly line above it to get a better picture of it
To determine the reason for the step taken in the proof, we need to examine the information given.
Given:
- <1 is the supplement of <2
- <3 is the supplement of <4
- <2 ≅ <4
We are trying to prove that <1 ≅ <3.
To find the reason for the step taken, we can compare the given information to the properties or theorems of angles.
Applying the given information, we can see that angles <2 and <4 are supplementary angles. According to the definition of supplementary angles, the sum of their measures is 180 degrees.
Since <2 ≅ <4, their measures are equal. Therefore, if two angles are equal and supplementary, it means they are congruent to each other.
The property or theorem that we are utilizing in this proof is the congruent supplements theorem, which states that if two angles are supplements of congruent angles, then they are congruent themselves.
So, the reason for the step taken in this proof is the congruent supplements theorem (b).