You have to be well aware of the star chep machine. Once you put an **A4 page** inside the machine and activate it, you acquire an similar copy of that page. If you rotate or upper and lower reversal the page, that will remain the exact same as the original page. Even if you cut them out, you have the right to line them increase again easily. We can say the pages space **similar or congruent.You are watching: Which pair of triangles can be proved congruent by sss**

Further, the A4 web page is in a rectangular shape, so once you cut it diagonally, you will get the triangle. If you cut both the photocopies in the exact same manner, you will check out both of them type the exact same kind the a triangle, which has actually the exact same sets that angles and sides.

## What is a Congruent Triangle?

You must be well mindful of a triangle by currently — that it is a 2-dimensional figure with 3 sides, 3 angles, and also three vertices. 2 or more triangles are claimed to it is in congruent if their corresponding sides or angles room the side. In other words, **Congruent triangles have the very same shape and dimensions**.

**Congruency is a term supplied to define two objects through the very same shape and also size**. The symbol because that congruency is **≅**. In triangles, we use the abbreviation **CPCT** to display that the **Corresponding parts of Congruent Triangles** room the same.

Congruency is no calculated no one measured however is determined by visual inspection. Triangle can become congruent in three different motions, namely, rotation, reflection, and also translation.

## What is Triangle Congruence?

Triangle congruences room the rule or the techniques used come prove if 2 triangles space congruent. 2 triangles are claimed to be congruent if and only if we have the right to make one of them superpose ~ above the various other to cover that exactly.

**These 4 criteria used to test triangle congruence include**:

Side – side – next (**SSS**), side – angle – next (**SAS**), angle – next – angle (**ASA**), and also Angle – angle – next (**AAS**).

There are much more ways to prove the congruency the triangles, but in this lesson, we will certainly restrict ourself to this postulates only.

Before going right into the **detail of this postulates of congruency**, that is important to know how to mark different sides and also angles with a certain sign which reflects their congruency. Girlfriend will often see the sides and angles the a triangle are marked with little tic marks come specify the sets of congruent angles or congruent sides.

You will see in the diagrams below that the sides with one tic mark are the the very same measurement, the sides with two tic marks also have the very same length, and also the sides v the tic marks room equal. The exact same goes for the angles.

### Side – angle – Side

**Side Angle next (SAS) is a preeminence used come prove even if it is a given collection of triangles room congruent**. In this case, 2 triangles space congruent if 2 sides and also one had angle in a provided triangle room equal come the matching two sides and also one included angle in an additional triangle.

Remember the the consisted of angle have to be developed by the 2 sides because that the triangles to be congruent.

*Illustration the SAS rule:*

Solution

*∆ABC **≅** ∆PQR*

Therefore,

55 ° + 65 ° + (2x + 30) ° = 180°

120° + 2x + 30° = 180°

150° + 2x = 180°

2x = 30°

x = 15°

*Example 3*

Describe the kind of congruence in 2 triangles offered by;

∆ ABC, abdominal = 7 cm, BC = 5 cm, ∠B = 50° and also ∆ DEF, DE = 5 cm, EF = 7 cm, ∠E = 50°

Solution

Given:

AB = EF = 7 cm,

BC = DE = 5 cm and

∠B =∠E = 50°

Therefore, ∆ABC ≅ ∆FED (SAS)

**Real-life instances of congruent objects (h3)**

There room infinite instances of congruent objects i beg your pardon we see or observe in our daily life. A basic example is a load of biscuits through all biscuits the the very same size and also shape if they are not broken. We deserve to say all the biscuits are congruent.

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*A couple of more examples of congruency are:*

** **