Identical Twins have the precise same size and shape, and we instantly recognise that the two of them are exactly the same.

When 2 items have actually the exact same size and also shape, we say the they are “Congruent”.

This class is all around “Congruent Triangles”, eg. Bag of triangles which have the specific same size and also shape.

Congruent triangle are an essential part that our daily world, particularly for reinforcing many structures.


Here room a usual pair the Congruent Triangles


Two triangles are congruent if castle are completely identical.

You are watching: Examples of congruent triangles in real life

This means that the matching sides must be the exact same length and also the corresponding angles should be the very same size.

The identical (eg.”Congruent”) Triangles deserve to be in different positions, (or orientations), and also still be the exact same size and also shape.

The place of the matching Triangles go not affect the reality that they are identical, or “Congruent”.


Introductory video clip About Congruency

The following video clip by Mr invoice Konst around Congruence, covers the “SSS rule for Triangles”, and covering Quadrilaterals and also some amazing optical illusions.

Shortcut Rules because that Congruent triangle

It turns out the we execute not have actually to check all the sides and angles of two Triangles to work out that they space Congruent.


There are four “Shortcut Rules” because that Congruent Triangles the we will be covering in this lesson.

The first of this “Shortcut Rules” is the “Side next Side”, or “SSS” Rule.

SSS – next Side Side ascendancy for Triangles

We deserve to actually use just the three sides to work out if two triangles room congruent.

This is called “SSS” or the “Side next Side Rule”.


In diagrams, the actual worths of the sides are occasionally not given.

Instead we have markers to present where the matching same length sides space on the two triangles.

For these Triangles us can apply the “SSS” rule, as long as we have actually all 3 sides corresponding each other on the two triangles.


Symbols supplied in Congruency

There is a one-of-a-kind symbol we usage to show that Triangles space Congruent, the is prefer an equates to sign with an extra line included on optimal of it.

This triple ine price is what we usage in Australia; yet some other countries use an amounts to sign through a squiggly “tilda” line included to the optimal of it.

In addition, Triangles space usually labelled with capital alphabet letters.

When us say the Triangles are Congruent making use of their letters, we must make certain the order of the letters matches the path around the 2 triangles correctly.

This is displayed in the adhering to example.


We need to be cautious with the labelling once our Triangles room in various positions.

Eg. We have to make sure the order of the letters matches going roughly the two triangles in the exact same order the sides. Going A come B to C need to be the specific same course as D to E to F.


SAS – side Angle Side preeminence for triangle

Two Triangles will certainly be congruent if two matching sides have actually equal lengths andthe angle contained by these sides is the same.


The following video covers the “SSS” and “SAS” Rules because that Congruent Triangles.

The American teacher law the videos walk not constantly use the most correct language, but he is enthusiastic and explains his instances well.

AAS – edge Angle Side ascendancy for triangles

Two triangles room congruent if two corresponding angles are equal and a corresponding side is same in length.


There is additionally an old “ASA” Angle side Angle Rule; however this has actually been carried in to be component of the “AAS” Rule.


It is fairly okay to use the “ASA” rule if the order of the items is “ASA” as presented in the over diagram.

However, most people these days simply use “AAS”, so the there is one less congruency ascendancy to memorise.

The adhering to “YayMath” 26 minute offers a an extensive lesson on the ASA and also AAS Rules.

RHS – best Angle Hypotenuse Rule

Any 2 Right-Angled 90 degree Triangles room congruent if the hypotenuse and one pair of equivalent sides room equal in length.


This preeminence works due to the fact that of Pythagoras Theorem because that 90 degree Triangles.

Pythagoras Rule way that the missing side lengths need to be equal, therefore we space indirectly using the “SSS” dominion here.

Why the SSA preeminence Does not Exist

The following video clip shows why there is no an SSA rule for congruent triangles.

Triangle Rules an overview

There are four rules the we usage to identify if Triangles room congruent: SSS, SAS, AAS, and also RHS.

These are displayed in the diagram below:


Congruent triangle Music Videos

Here is a quick tiny tune through Abbie around the Triangle Rules, mentioning exemption of the invalid Angle next Side “Donkey Rule”.

This following one is a heavy metal Parody (sounds a bit like a Joan Jet song):

Congruent Triangles instances

The following examples display the compelled working out for demonstrating that a pair the Triangles room identical.




Composite Shapes instances

The following video shows some more complicated examples, whereby triangle sides space joined with each other to other triangles and shapes.

In the next two examples, Congruent triangles are discovered within the provided Geometric Shapes, which permits side lengths to it is in proven as equal.

Rules for angle in Parallel present are also used, in particular, the following alternating Interior angle Rule:


This first example is the classic “Bow Tie” shaped concern for join congruent triangles.


The next example requires two triangles sharing the diagonal line of a Parallelogram.


Congruent triangles Worksheets

The adhering to worksheet has simple multiple an option questions on Congruent Triangles.

(There are answers top top the last page of the PDF document).

The following video has one worked instance to gain you started.

Click the link listed below to carry out this worksheet:

Basic Level Worksheet

The complying with worksheet has actually medium level of challenge multiple selection questions ~ above Congruent Triangles.

(There are answers on the last web page of the PDF document).

The following video has one worked instance to acquire you started.

Click the link listed below to do this worksheet:

Medium Level Worksheet

This last worksheet has challeging multiple selection questions ~ above Congruent Triangles.

(There room answers ~ above the last page of the PDF document).

The following video clip has one worked instance to obtain you started.

Click the link below to perform this worksheet:

Challenging Worksheet

Congruent Triangles games


The over game is a equivalent game with numerous levels of difficulty.

It is more like a Quiz 보다 a Game, yet will help you discover congruent triangles.

Click the link below to play this game.

This next game involves dropping the shapes into the correct boxes making use of the arrow keys.

It also contains multiple choice questions that need to be answered.


Click the link listed below to pat this game.

The adhering to is an activity where we obtain to build congruent triangles based upon the congruency rule we pick to work with.


Click the link below to play this game.

This last game is a Jeapordy Game, however is very slow to load up.


Click the link listed below to play this game.

See more: Biological Community Of Interacting Organisms And Their Physical Environment ?

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