unit 1 geometry basics homework 2 segment addition postulate answers

Segment Addition Postulate

The segment addition postulate in geometry is applicable on a line segment containing three collinear points. It states that if there are two given points on a line segment A and C, then point B lies on the same line segment somewhere between A and C only if the sum of AB and BC is equal to AC.

By applying the segment addition postulate, we can precisely determine the length of a line segment when given specific measurements of its parts. Also, this postulate enables us to divide a line segment into different sections and explore the relation (ratios) between their lengths.

Segment Addition Postulate Definition

The segment addition postulate states that if a line segment has two endpoints, A and C, a third point B lies somewhere on the line segment AC if and only if the equation AB + BC = AC is satisfied. Look at the image given below to have a better understanding of this postulate.

If we carefully look at its name "Segment Addition Postulate", it is very easy to understand.

• A segment, here, means a line segment. It emphasis that this postulate is applicable only on a line segment, and not on a ray or a line . A line segment is part of a line bounded by two defined endpoints. We can have an infinite number of points between the endpoints of a segment.
• The "addition" means that we are adding the distances between points.
• Finally, "postulate" means this axiom is taken as a fact or valid without any proof.

Another way of stating the segment addition postulate is that if point B lies on the line segment AC, then AB + BC = AC.

Segment Addition Postulate Formula

If the end-points of a line segment are denoted as A and C, and there lies a point B on the line segment, then the segment addition postulate formula is given as AB + BC = AC.

Further, extending this theorem to two points, If there are two points B and D on the segment, we will have the formula as AB + BD + DC = AC.

☛ Related Topics:

• Segment Addition Postulate Worksheets
• Difference Between Line and Line Segment
• Line Segment

Segment Addition Postulate Examples

Example 1: In the given figure, if B is the mid-point of line segment AC, find the length of segment AC.

By using the segment addition postulate, we know that the sum of segments AB and BC is equal to AC. It can be written mathematically as AB + BC = AC. Also, B is the midpoint of AC. It implies AB = BC.

⇒ 3x = 4x-6

⇒ 6 = 4x - 3x

Now, put the value of x in the equation AB + BC = AC.

AC = 3x + 4x - 6

⇒ AC = 7x - 6

⇒ AC = 7 × 6 - 6

⇒ AC = 42 - 6

Answer: ∴ The length of the segment AC is 36 units.

Example 2: Find whether Q is the mid-point of segment PR or not, if the length of PR is 45 units. [Refer to the figure below]

Solution: There are three collinear points on the given segment which are points P, Q, and R. By using the segment addition postulate, we know that PQ + QR = PR. Substitute the value of PR as 45 units, we get,

PQ + QR = 45

⇒ 9x + 7 + (-3x+20) = 45

⇒ 9x - 3x + 7 + 20 = 45

⇒ 6x + 27 = 45

Now, let us find the values of PQ and QR.

PQ = 9x + 7 = 9 (3) + 7 = 34 units

QR = -3x+20 = -3 (3) + 20 = 11 units

Answer: ∴ PQ ≠ QR. Q is not the midpoint of segment PR.

Example 3: On a line segment XY, if Z is between X and Y and XY = 25. What will be the expression to find the value of XZ?

Solution: It is given that point Z is between X and Y, so by using the segment addition postulate, we have XZ + ZY = XY. The value of XY is given as 25. So, the expression to find the value of XZ is 25 - ZY.

Answer: ∴ 25 - ZY is the required expression.

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Practice Questions on Segment Addition Postulate

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FAQs on Segment Addition Postulate

What is segment addition postulate in geometry.

The segment addition postulate in geometry is the axiom which states that the length of a line segment divided into smaller pieces is the sum of the lengths of all those smaller segments. So, if we have three collinear points A, B, and C on segment AC such that B is somewhere between A and C, then AB + BC = AC. It is a mathematical fact that can be accepted without proof.

What are the Two Conditions of the Segment Addition Postulate?

The two conditions of the segment addition postulate are given below:

• A point P lies on a segment MN if and only if points M, P, and N are collinear taken in order.
• The distance between MP and PN must be equal to MN.

What are the Examples of Segment Addition Postulate?

As per the segment addition postulate, if we have an iron rod of length 30 inches that is cut into two parts where the length of one part is 14 inches, it means the length of the other part of the rod is 30 - 14 = 16 inches.

What is a Segment Addition Postulate Used For?

We can apply this postulate in calculating the missing lengths. It can be used to find the sum of the smaller parts of a segment to find the total length. The segment addition postulate has its applications in construction, architecture, design, etc.

How to Solve for x with Segment Addition Postulate?

If we have a missing length, let's say x, and we know the total length and the length of the other part of the segment, then we can apply the segment addition postulate to find x. For example, if AB = 3, BC = x, and AC = 5, then we can find x by subtracting AB from AC. This implies AC - AB = 5 - 3 = 2 = BC. i.e., x = 2.

How to Use the Segment Addition Postulate to Show that ae=ab+bc+cd+de?

If a segment AE has three points on it, marked as B, C, and D in order, then according to the segment addition postulate, their sum is equal. So, AE = AB + BC + CD + DE. This is possible by applying the postulate for more than one time.

What is Segment Addition Postulate in Proofs?

The segment addition postulate does not require any proof. It is accepted as a mathematical fact. But many times, we use this axiom in stating proofs for line segments. One such proof is given as "If two congruent segments are added to the line segments of the same length, then their sum is also equal."

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Unit 1 Geometry Basics Homework 2 Segment Addition Postulate

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Some of the worksheets for this concept are The segment addition postulate date period, Geometry, Geometry unit 1 workbook, Segment addition answers, Geometry chapter 2 reasoning and proof, Identify points lines and planes, 1 introductionto basicgeometry, Infinite geometry.

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1. The Segment Addition Postulate Date Period

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Geometry Basics (Geometry Curriculum - Unit 1) | All Things Algebra®

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This Geometry Basics Unit Bundle contains guided notes, homework assignments, three quizzes, dictionary, study guide and a unit test that cover the following topics:

• Points, Lines, and Planes

• Segment Addition Postulate

• The Distance Formula

• The Midpoint Formula

• Partitioning a Segment

• Naming and Classifying Angles

• Angle Addition Postulate

• Angle Relationships (Adjacent, Vertical, Complementary, Supplementary, Linear Pair)

• Solving for Missing Measures using Algebra

• Special Relationships: Perpendicular and Angle Bisectors

• Constructions (Perpendicular bisectors, perpendicular line through a point on the line, perpendicular line through a point not on the line, line parallel to a given line through a given point, angle bisector, congruent angles)

Note: This unit was updated on 8/25/19 to include partitioning a segment. If you do not teach this topic, I included the old unit without this topic in the download as well.

ADDITIONAL COMPONENTS INCLUDED:

(1) Links to Instructional Videos: Links to videos of each lesson in the unit are included. Videos were created by fellow teachers for their students using the guided notes and shared in March 2020 when schools closed with no notice.  Please watch through first before sharing with your students. Many teachers still use these in emergency substitute situations. (2) Editable Assessments: Editable versions of each quiz and the unit test are included. PowerPoint is required to edit these files. Individual problems can be changed to create multiple versions of the assessment. The layout of the assessment itself is not editable. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own.

(3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. Each page is set to the background in Google Slides. There are no text boxes;  this is the PDF in Google Slides.  I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead! 

This resource is included in the following bundle(s):

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More Geometry Units:

Unit 2 – Logic and Proof

Unit 3 – Parallel and Perpendicular Lines

Unit 4 – Congruent Triangles

Unit 5 – Relationships in Triangles

Unit 6 – Similar Triangles

Unit 7 – Right Triangles and Trigonometry Unit 8 – Polygons and Quadrilaterals

Unit 9 – Transformations

Unit 10 – Circles

Unit 11 – Volume and Surface Area Unit 12 – Probability

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