Embedded Files
The Segment Addition Postulate states that given three collinear points, a segment addition statement can be written. Consider the following geometric figure. Points J, K, and L are collinear and point K is between J and L.
CONDITIONAL STATEMENT: If point K is between points J and L, then JK + KL = JL.
CONVERSE STATEMENT: If JK + KL = JL, the point K is between points J and L.
BI-CONDITIONAL STATEMENT: Point K is between points J and L, if and only if JK + KL = JL.
The conditional , converse, and bi-conditional statements above are typical ways to communicate mathematical concepts. Whenever both a conditional statement and its converse statement are true, then a bi-conditional statement may be written. Bi-conditional statements are the basis of a definition.
Ex 1 – Solution
Ex 1 – Solution
Using the Segment Addition Postulate we can write : AB + BC = AC.
Then, by the Substitution Property of Equality, we can replace AB with 27 and AC with 43. This yields the equation : 27 + BC = 43
Next, by Subtraction Property of Equality, we can subtract 27 from both sides of the equation. The result finds that the length is BC = 16.
Ex 2 – Solution
Ex 2 – Solution
Using the Segment Addition Postulate we can write : XY + YZ = XZ.
Next, with the Substitution Property of Equality, we can replace XY with 4x - 13, replace YZ with 3x + 5, and replace XZ with 5x + 3.
This yields the following equation : (4x - 13) + (3x + 5) = (5x + 3)
Combining like terms will simplify the equation as : 7x - 8 = 5x + 3
Solve the equation to obtain x = 5.5
Substitute x = 5.5 into the expression for XZ to see that XZ = 5(5.5) + 3 or XZ = 30.5
Video Tutorials
Video Lecture – Segment Addition Postulate
Guided Construction – Congruent Segment
Page updated
Google Sites
Report abuse