In this chapter we will learn about SSS postulate of congruent triangles along with the solved examples.

This theorem is used to prove congruency of two triangles.

Let us first understand the basics of congruent triangles.

## What are congruent triangles?

Two triangles are said to be congruent when **they have equal angle and sides**.

This means that when we place congruent triangles against each other they will fully overlap each other.

## What is SSS Postulate ?

Here **SSS** stands for** side – side – side of triangle**.

The postulate states that if** all the three sides of a triangle are equal** **to the sides of other triangle** then the given triangles are congruent.

For Example;

Consider the triangles ABC and PQR

We can see that;

AB = PR = 4 cm

BC = QR = 3 cm

AC = PQ = 3.6 cm

Hence by SSS congruency, we can say that both the triangles are congruent.

▵ABC \mathtt{\cong } ▵PRQ

Since both the triangles are congruent, it means that they have equal sides and angles and can perfectly overlap each other.

I hope the concept is clear, let us see some solved problems.

## SSS Postulate – Solved Problems

(01) Check if the triangles ABC and ADC are congruent or not.

**Solution**

In triangle ABC and ADC.

AB = DC = 2.7 cm

AD = BC = 4.1 cm

AC = CA = Common Side

Hence by SSS congruency, both the triangles are congruent.

▵ABC \mathtt{\cong } ▵DCA

**(02) Find the value of ∠DAB ?**

**Solution**

Compare triangle ABD and CBD.

AD = CD = 5.2 cm

AB = CB = 3.7 cm

BD = DB = Common Side

Hence by SSS congruency postulate, both the triangles are congruent.

So, ▵ABD \mathtt{\cong } ▵CBD

We know that congruent triangles have equal corresponding sides and corresponding angles.

So,

We know that congruent triangles have equal corresponding sides and corresponding angles.

So, **∠DCB = ∠DAB = 33 degree.**

**(03) Find the value of ∠ACB ?**

**Solution**

Take triangle ABC and DCB.

AB = DC = 5 cm

BC = CB = Common side

AC = DB = 9 cm

Hence, both triangle ABC and DCB are congruent.

So, ▵ABC \mathtt{\cong } ▵DCB

We know that congruent triangles have equal corresponding sides and angles.

Hence, **∠DBC = ∠ACB = 40 degree**.

(04) Study the below triangles and check which of the below option is correct.

(i)▵ABO \mathtt{\cong } ▵COA

(ii)▵ABO \mathtt{\cong } ▵ACO

(iii) ▵ABO \mathtt{\cong } ▵AOC

**Solution**

Consider the two triangles ABO and ACO

AB = AC = 8.5 cm

BO = CO = 4 cm

AO = OA = Common sides

By SSS postulate, ▵ABO \mathtt{\cong } ▵COA

**Hence option (ii) is correct**.**Note:**

While mentioning the congruent triangles, **the sequence of alphabet is very important**.

In ▵ABO \mathtt{\cong } ▵COA.**Observe the linear arrangement of alphabets** in both triangles

Side AB = CO { First two letters of triangles }

Side BO = OA { Last two letters }

Side OA = CA { Last & First letters }

Hence in proper sequence, the sides are equal to each other.

**If you take first option** ▵ABO \mathtt{\cong } ▵COA

Side AB = CO { which is not correct }

Hence, **the first option is wrong representation**.

**Now look at third option**;▵ABO \mathtt{\cong } ▵AOC

Taking first two letters;

Side AB = AO { which is not correct }**Hence, third option is wrong representation**.

**(05) Find the value of ∠BAO ? **

**Solution**

Consider the triangles BAO and CDO

side BA = CD

side OA = OD

side BO = CO

By SSS congruency, ▵BAO \mathtt{\cong } ▵CDO

We know that in congruent triangles, angles are equal.

Hence, **∠BAO** = **∠OCD** = 60 degree

**Next chapter** : **Understand SAS congruency in detail**