if the measure of angle 1 + the measure of angle 2 = 180 and the measure of angle2 + the measure of angle 3 = 180 , then angle 2 is equivilent to angle 3
what property justifies the statement?
Well, this seems like a classic case of "Angles with identity crisis." It appears that both angle 2 and angle 3 are in deep denial about their true identities. The property that justifies the statement is the Transitive Property of Equality, which basically says that if angle 1 + angle 2 = 180 and angle 2 + angle 3 = 180, then angle 1 + angle 2 + angle 3 = 360. Since the sum of all angles in a triangle is 180 degrees, angles 2 and 3 must be equivalent to each other. It's time for them to embrace their true identities and let go of their doubts!
The property that justifies the statement is the Transitive Property of Equality.
To understand why, let's break down the problem step by step:
1. We are given that the measure of angle 1 + the measure of angle 2 is equal to 180 degrees.
2. We are also given that the measure of angle 2 + the measure of angle 3 is equal to 180 degrees.
3. By adding these two equations together, we can simplify it as follows:
(measure of angle 1 + measure of angle 2) + (measure of angle 2 + measure of angle 3) = 180 + 180
measure of angle 1 + measure of angle 2 + measure of angle 2 + measure of angle 3 = 360
measure of angle 1 + 2 * measure of angle 2 + measure of angle 3 = 360
measure of angle 1 + measure of angle 3 + 2 * measure of angle 2 = 360
measure of angle 1 + measure of angle 3 = 360 - 2 * measure of angle 2
Now, we can see that the measure of angle 1 + measure of angle 3 is equal to a constant value of 360 - 2 * measure of angle 2.
Therefore, if angle 1 and angle 3 have a fixed sum, then the value of angle 2 has to remain the same in order to maintain the constant sum of 360.
In mathematical terms, we can express this using the Transitive Property of Equality, which states that if "a = b" and "b = c," then "a = c." In this case, angle 1 + angle 3 = 360 - 2 * angle 2, and angle 2 + angle 3 = 180. By applying the Transitive Property, we can conclude that angle 2 is equivalent to angle 3.