Which reason justifies that BD = BC + CD?
a. Addition property
b. Symmetric Property
c. Segment Addition Postulate
d. Ruler Postulate
I't thinking its Addition Property but then again I'm probably completely wrong...
since we're dealing with line segments, I'd say C
The correct answer is c. Segment Addition Postulate.
The Segment Addition Postulate states that if three points A, B, and C are collinear and B is between A and C, then the distance between A and C is equal to the sum of the distances between A and B and B and C.
In this case, BD = BC + CD because B is between D and C, and the distance between D and C can be determined by adding the distance between D and B to the distance between B and C, according to the Segment Addition Postulate.
To determine which reason justifies that BD = BC + CD, let's break down the options:
a. Addition property: The addition property states that if you add the same quantity to both sides of an equation, the equation remains true. However, this property does not directly apply to BD = BC + CD.
b. Symmetric property: The symmetric property states that if a = b, then b = a. This property is not directly related to the given equation.
c. Segment Addition Postulate: The segment addition postulate is the most suitable justification for BD = BC + CD. According to the segment addition postulate, if three points are collinear (in this case, B, C, and D), then the sum of the lengths of the smaller segments formed by those points is equal to the length of the entire segment. Therefore, BD = BC + CD.
d. Ruler postulate: The ruler postulate states that points can be paired with real numbers so that every point corresponds to a unique real number and vice versa. While the ruler postulate is applicable to measurement, it does not directly justify BD = BC + CD.
Considering the explanations provided, the correct justification for BD = BC + CD is the segment addition postulate (c).