Mathematics
Grade 10
15 min
Additive property of length
Additive property of length
What you'll learn
- Solve one-step word problems involving addition and subtraction of money amounts up to $100 with 80% accuracy.
- Identify the key information (numbers and operations) needed to solve money-related word problems in at least 4 out of 5 examples.
- Apply the correct dollar and cent notation ($ and .) when writing solutions to money word problems with 100% accuracy.
- Explain the steps used to solve a two-step money word problem to a partner, using appropriate mathematical vocabulary (e.g., sum, difference, total).
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the Segment Addition Postulate and the concept of betweenness of points.
Apply the additive property of length to calculate the length of a segment given the lengths of its component parts.
Set up and solve algebraic equations to find unknown segment lengths.
Use segment lengths to determine if three points are collinear.
Correctly use the Segment Addition Postulate as a justification in geometric proofs.
Differentiate between the notation for a line segment (e.g., \overline{AB}) and its length (e.g., AB).
Ever planned a road trip with a stop in the middle? How do you find the total distance? 🗺️ The simple act of adding the two legs of the journey is a real-world example of the additive property of length!
This tutorial explores the Segment Additi...
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Key Concepts & Vocabulary
TermDefinitionExample
PointA specific location in space. It has no dimension (no length, width, or height) and is represented by a dot.In the diagram, A, B, and C are all points.
Line SegmentA part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. It is denoted by \overline{AB}.A piece of a ruler from the 2 cm mark to the 5 cm mark is a line segment.
Length of a SegmentThe distance between the endpoints of a line segment. It is a positive number. The length of \overline{AB} is denoted by AB (without the bar).If \overline{AB} spans from x=3 to x=8 on a number line, its length AB is 5 units.
Collinear PointsPoints that lie on the same straight line.If you can draw a single straight line that passes through points P, Q, and R, t...
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Core Formulas
Segment Addition Postulate
If B is a point on \overline{AC} between A and C, then AB + BC = AC.
This postulate allows you to find the total length of a segment by adding the lengths of its smaller, adjacent, and collinear parts. It is the core of the additive property of length.
Converse of the Segment Addition Postulate
If three points A, B, and C satisfy the equation AB + BC = AC, then B must lie on the line segment \overline{AC}.
This rule is used to prove that three points are collinear. If the sum of the two smaller distances equals the largest distance, the points form a single straight line segment.
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Challenging
Points A, B, and C are located on a number line at coordinates x-7, x, and 3x-4 respectively. If B is between A and C, what is the length of \overline{AC}?
A.3
B.12
C.9
D.15
Challenging
Points A, B, and C are collinear with B between A and C. Point D is not on line AC. Which statement must be true about the lengths in triangle ABD?
A.AB + BD = AD
B.AB + BD > AD
C.AB + AD < BD
D.AB = BD
Challenging
For three distinct points A, B, and C, the distance AB = 10 and the distance BC = 4. Which of the following is NOT a possible value for the distance AC?
A.7
B.13.5
C.6
D.15
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Frequently asked questions
What grade level is "Additive property of length"?
Additive property of length is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Additive property of length?
You'll be able to: Solve one-step word problems involving addition and subtraction of money amounts up to $100 with 80% accuracy; Identify the key information (numbers and operations) needed to solve money-related word problems in at least 4 out….
Is "Additive property of length" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Additive property of length?
This lesson includes 49 practice questions across multiple difficulty levels, each with instant feedback and explanations.