precisely the same three sides and also precisely the same three angles.

But us don"t have to know all three sides and all three angles ...usually three out of the six is enough.

There are five ways to uncover if two triangles space congruent: SSS, SAS, ASA, AAS and HL.

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1. SSS (side, side, side)

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SSS represents "side, side, side" and means that we have actually two triangles v all 3 sides equal.

For example:

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is congruent to:
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(See fixing SSS triangle to find out more)


If three sides the one triangle room equal to 3 sides of another triangle, the triangles are congruent.


2. SAS (side, angle, side)

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SAS stands for "side, angle, side" and way that we have two triangles wherein we know two sides and also the contained angle are equal.

For example:

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is congruent to:
*

(See addressing SAS triangles to find out more)


If 2 sides and the included angle of one triangle room equal come the equivalent sides and also angle of another triangle, the triangles room congruent.


3. ASA (angle, side, angle)

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ASA stands for "angle, side, angle" and way that we have actually two triangles whereby we recognize two angles and also the had side are equal.

For example:

*
is congruent to:
*

(See solving ASA triangle to discover out more)


If two angles and also the consisted of side the one triangle are equal come the equivalent angles and also side of another triangle, the triangles space congruent.


4. AAS (angle, angle, side)

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AAS means "angle, angle, side" and method that we have two triangles whereby we understand two angles and also the non-included side room equal.

For example:

*
is congruent to:
*

(See resolving AAS triangles to discover out more)


If 2 angles and the non-included next of one triangle are equal to the corresponding angles and side of an additional triangle, the triangles space congruent.


5. HL (hypotenuse, leg)

This one applies only to appropriate angled-triangles!

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or
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HL means "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two political parties are called "legs")

It method we have two right-angled triangle with

the same length of hypotenuse and also the same size for one of the other two legs.

It doesn"t matter which leg due to the fact that the triangles can be rotated.

For example:

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is congruent to:
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(See Pythagoras" to organize to find out more)


If the hypotenuse and also one leg of one right-angled triangle are equal to the matching hypotenuse and leg of one more right-angled triangle, the 2 triangles are congruent.


Caution! Don"t use "AAA"

AAA method we are offered all three angles of a triangle, but no sides.

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This is not sufficient information to decision if two triangles are congruent!

Because the triangles can have the same angles however be different sizes:

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is not congruent to:
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Without knowing at least one side, us can"t be certain if 2 triangles space congruent.


Congruent Congruent Triangles comparable Similar triangles Finding comparable Triangles Trigonometry index