Using the Segment Addition Postulate Which is True

August 27, 2022 admin 117 Views

Using the Segment Addition Postulate Which is True

Segment Addition Postulate

The segment addition postulate in geometry is applicative on a line segment containing iii collinear points. The segment improver postulate states that if there are ii given points on a line segment A and C, then point B lies on the same line segment somewhere between A and C simply if the sum of AB and BC is equal to Ac.

1.	Segment Addition Postulate Definition
2.	Segment Add-on Postulate Formula
3.	FAQs on Segment Addition Postulate

Segment Improver Postulate Definition

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

If we carefully expect at its name “Segment Addition Postulate”, it is very easy to understand. A segment, here, means a line segment. Information technology emphasis that this postulate is applicable simply on a line segment, and not on a ray or a line. A line segment is part of a line bounded by ii defined endpoints. Nosotros can accept an space number of points between the endpoints of a segment. The “add-on” means that nosotros are calculation the distance betwixt points. And “postulate” ways this axiom is taken as a fact or valid without whatsoever proof.

Another way of stating the segment add-on postulate is that if betoken B lies on the line segment Ac, and then AB + BC will exist equal to Ac.

Segment Addition Postulate Formula

If the end-points of a line segment are denoted every bit A and C, and in that location lies a point B on the line segment, so the
segment addition postulate formula
is given as AB + BC = AC. If in that location are two points B and D on the segment, we will accept the formula as AB+BD+DC = AC.

Segment Addition Postulate Related Topics

Check these interesting articles related to the concept of segment addition postulate in geometry.

Segment Addition Postulate Worksheets
Lines
Difference Between Line and Line Segment
Line Segment
Euclid’due south Geometry

Segment Addition Postulate Examples

Case 1: In the given effigy, if B is the mid-indicate of line segment AC, notice the length of segment Ac.

Solution:
By using the segment addition postulate, we know that the sum of segments AB and BC is equal to AC. It can exist written mathematically as AB + BC = AC. Also, B is the mid-point of AC. It implies AB = BC.

AB = BC

⇒ 3x = 4x-6

⇒ 6 = 4x – 3x

⇒ x = 6

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

AC = 3x + 4x – 6

⇒ AC = 7x – vi

⇒ Air-conditioning = 7 × six – 6

⇒ AC = 42 – half dozen

⇒ AC = 36

Therefore, the length of the segment Air-conditioning is 36 units.
Instance 2: Find whether Q is the mid-point of segment PR or not, if the length of PR is 45 units. [Refer to the effigy below]

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

PQ + QR = 45

⇒ 9x + 7 + (-3x+twenty) = 45

⇒ 9x – 3x + 7 + 20 = 45

⇒ 6x + 27 = 45

⇒ 6x = 18

⇒ x = 3

At present, allow united states discover the values of PQ and QR.

PQ = 9x + seven = 9 (three) + 7 = 34 units

QR = -3x+xx = -three (3) + twenty = xi units

Therefore, PQ ≠ QR. Q is not the midpoint of segment PR.
Example 3: On a line segment XY, if Z is between 10 and Y and XY = 25. What will exist the expression to find the value of XZ?

Solution:
It is given that point Z is between Ten and Y, then by using the segment improver postulate, we take XZ + ZY = XY. The value of XY is given as 25. So, the expression to find the value of XZ is 25 – ZY. Therefore, 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 Add-on Postulate in Geometry?

The segment addition postulate in geometry is the axiom which states that a line segment divided into smaller pieces is the sum of the lengths of all those smaller segments. So, if we take iii collinear points A, B, and C on segment Air conditioning, information technology means AB + BC = Air conditioning. Information technology is a mathematical fact that tin be accepted without proof.

What are the Ii Conditions of the Segment Addition Postulate?

The ii conditions of the segment addition postulate are given beneath:

A point P lies on a segment MN if and only if points K, P, and Due north are collinear.
The altitude between MP and PN must be equal to MN.

What are the Examples of Segment Addition Postulate?

Every bit per the segment addition postulate, if we have an iron rod of length thirty inches, and it is cutting into two parts. If the length of one part is 14 inches, it means the length of the other part of the rod is 30 – 14 = xvi inches. This is one of the examples of segment add-on postulate.

What is a Segment Add-on Postulate Used For?

We tin can utilize this postulate in calculating the missing lengths. It tin can exist used to find the sum of the smaller parts of a segment to notice the total length. The segment addition postulate has its applications in construction, architecture, designing, etc.

How to Solve for x with Segment Addition Postulate?

If we have a missing length, allow’due south say x, and nosotros know the full length and the length of the other part of the segment, so nosotros tin apply the segment addition postulate to find 10. For instance, if AB = iii, BC = ten, and AC = 5, then we can find x by subtracting AB from AC. This implies Air conditioning – AB = 5 – 3 = two.

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

If a segment AE has iii points on it, marked as B, C, and D, then according to the segment addition postulate, their sum is equal. And then, AE = AB + BC + CD + DE.

What is Segment Addition Postulate in Proofs?

The segment add-on postulate does not require any proof. It is accepted as a mathematical fact. Simply many times, we use this axiom in stating proofs for line segments. 1 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.”