Transitive Property Of Equality Definition

Transitive Property of Equality

Transitive belongings of equality states that if two numbers are equal to each other and the second number is equal to the third number, then the first number is also equal to the third number. In other words, a = b, b = c, and then a = c. The transitive holding of equality is ane among the many properties of equality in math. This affiliate volition explore the transitive property meaning, transitive property of equality, transitive holding of angles, and transitive belongings of inequality.

one.	What is Transitive Property of Equality?
2.	Full general Formula of Transitive Property
3.	How to Use Transitive Property?
iv.	Proof of Transitive Property of Equality
5.	FAQs on Transitive Property of Equality

What is Transitive Holding of Equality?

The discussion transitive means transfer. If a, b, and c are iii quantities, and if a is related to b past some rule and b is related to c by the same rule, so a and c are related to each other by the aforementioned dominion, this belongings is called transitive property of equality. Allow us consider the quantities a = b and b = c. According to the symmetric belongings of equality, writing a = b is the same every bit b = a. Hence, we tin can say that b = a and b = c. However, the quantity b cannot be equal to two different quantities and a must be equal to c. Therefore, nosotros can say that a = c. Let u.s. wait at an example, presume Mary ate 2 hotdogs and Jake ate as many every bit Mary. This indicates that they ate the aforementioned number of hotdogs, according to the transitive property of equality.

Transitive Property of Equality

General Formula of Transitive Property

The formula for the transitive property of equality is: If a = b, b = c, then a = c. Here a, b, and c are three quantities of the same kind. This holding holds adept for real numbers. For example, if a is the measure out of an angle, and then b or c can't be the length of the segment.

Example: If x = k and one thousand = seven, so we can say ten = vii

The value 7 is transferred to x because x and 1000 are equal.

How to Employ Transitive Property?

To use the transitive belongings of equality, we demand three or more quantities for relating. This belongings can exist extended to the transitive property of angles and transitive holding of inequality as well.

Transitive Holding of Angles

According to the transitive property of congruence, if any ii angles, lines, or shapes are coinciding to a third angle, line, or shape respectively, and then the first ii angles, lines, or shapes are besides congruent to the third angle, line, or shape. For instance, if nosotros accept angles k and north such that thou = northward and north = p and m = 40°, then by the transitive property of angles, nosotros go p = 40°.

Transitive Property of Inequality of Real Numbers

Transitive property applies to inequality too and it states that, if nosotros have 3 real numbers x, y, and z such that, 10 ⩽ y and y ⩽ z, then x ⩽ z. For example, if we have a number p ⩽ 5 and 5 ⩽ q, then p ⩽ q. Permit united states look at another example, consider three people whose weights are unknown. Information technology is known that Sam weighs lesser than Rob and that Rob weighs bottom than Charlie. According to the belongings, nosotros can say that Sam likewise weighs lesser than Charlie.

Proof of Transitive Property of Equality

This holding cannot exist proved as information technology is an precept. However, ane of the well-known examples to prove the transitive holding of equality is by constructing an equilateral triangle using a ruler and compass. Hence, the aim is to show that the object synthetic is indeed an equilateral triangle with the help of the holding.

Construct a line segment AB with any measurement. Draw two circles where one circle crosses point A and the other circumvolve crosses point B. Where for one circle A is the center and AB is the radius and the other circle has B every bit the center and BA every bit the radius. Mark the intersection of the two circles every bit C. Complete the triangle by connecting A to C and B to C creating ABC. As we know that AB is the radius of 1 circle with A as the center, we can also consider Air conditioning as the radius of this circle making all the radii equal hence AB = AC (come across yellow circle). AB tin can also be considered as the radius for the other circle with centre B because according to the reflexive holding of addition, BA = AB. And for the aforementioned circle, BC can also exist considered as a radius hence AB = BC (see blue circle). Since AB = AC and AB = BC then we can say Air conditioning = BC according to the transitive property of equality. Therefore, all iii lines are equal to each other making ABC an equilateral triangle.

Transitive Property of Equality Proof

Important Notes

The transitive property of equality : If a = b and b = c, and then a = c
This property can be applied to numbers, algebraic expressions, and various geometrical concepts like congruent angles, triangles, circles, etc.

Related Topics

Listed beneath are a few topics related to transitive property of equality, accept a look.

Transitive Property of Congruence
Division Property of Equality
Addition Holding of Equality
Properties of Equality

Transitive Holding of Equality Examples

Instance i: The weight of a novel is the aforementioned as the weight of a storybook. The storybook weighs half the weight of a textbook. If the weight of the textbook is ane.6 lb, what is the weight of the novel?

Solution:

Let the weight of the novel, storybook, and textbook be (w)_northward, (due west)_s, (w)_t

The weight of the novel is the same equally the weight of the storybook. This indicates:

(w)_northward = (westward)_s (Equation one)

The storybook weighs one-half the weight of the textbook. This indicates:

(w)_s = one/2 × (w)_t (Equation ii)

Combining Equation 1 and Equation 2, we get,

(w)_n = one/ii × (west)_t (by transitive property)

= 1/ii × 1.6

= 0.8

Therefore, the weight of the novel is 0.8 lb.
Example 2: Lucy is given the information that line p II line q and line q II line r. She wants to know the relation between angles a and b. Can you help her detect the respond?

Solution: Since, line p Two line q and line q II line r, therefore, by transitive holding of equality line p II line r.

We know that when two lines are parallel, the corresponding angles are equal. Here, a and b are corresponding angles. Hence, they have equal measure.

Therefore, angle a = angle b.
Example three: Susan gives two hints to Mike and challenges him to find the relation between x and z. Hints : x+ y = z, z = 2y. Allow'southward find out how Mike can consummate this task.

Solution: Given,

x + y = z (Equation 1)

z = 2y (Equation 2)

Past transitive belongings of equality we get,

x + y = 2y

x = 2y - y

ten = y

Therefore, ten = y.

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Exercise Questions on Transitive Property of Equality

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FAQs on Transitive Property of Equality

What is Transitive Belongings Proof?

The transitive property is an axiom. That means, it is a universally accepted truth. Hence, we don't need to prove this property.

When Tin You Use Transitive Belongings?

We tin can utilise the transitive holding when we have three or more quantities of the aforementioned kind related past some dominion.

What is the Difference Between Transitive Property and Substitution Holding?

According to the commutation property, when two things are equal, then one of them can supplant the other in an expression i.eastward. a = b and x = a−3, and then ten = b−3

According to the transitive belongings, when two quantities are equal to the third quantity, then they are equal to each other i.east. a = b and a = c, and then b = c

How Do You Remember Transitive Property of Equality?

Transitive property of equality can exist seen among parallel lines along with numbers and equations.