Additive property of length

Key Notes :

The Additive Property of Length states that if Y is between X and Z, then XY + YZ = XZ.

Introduction:

  • The concept of the additive property of length is fundamental in geometry and mathematics.
  • It refers to the idea that the total length of a combination of line segments is equal to the sum of the lengths of the individual segments.
  • This property plays a crucial role in solving various geometric problems and real-world applications.

Explanation of the Additive Property:

  • Let’s consider two line segments, AB and BC, where point B is common to both.
  • According to the additive property of length, the length of the entire segment AC is equal to the sum of the lengths of AB and BC, denoted as AC = AB + BC.
  • This principle can be extended to more than two line segments, emphasizing that the total length is the sum of all individual lengths.

Learn with an example

1) If JK = 18 and KL = 8, what is JL?

Write your answer as a decimal or integer. __________

Use the diagram to write an equation and solve for JL.

JL = JK + KL Additive Property of Length

JL = 18 + 8 Plug in JK = 18 and KL = 8

JL = 26 Add

2) If CD = 15 and DE = 6, what is CE?

Write your answer as a decimal or integer. ___________

Use the diagram to write an equation and solve for CE.

CE = CD + DE Additive Property of Length

CE= 15 + 6 Plug in CD = 15 and  DE = 6

CE= 21 Add

3) If DE = 7 and  EF = 11, what is DF?

Write your answer as a decimal or integer. _________

Use the diagram to write an equation and solve for DF.

DF = DE + EF Additive Property of Length

DF = 7 + 11 Plug in DE = 7 and  EF = 11

DF = 18 Add

Let’s practice!