precisely the exact same three sides and specifically the very same three angles.

But us don"t have to know all three sides and also all 3 angles ...usually three out of the six is enough.

There are 5 ways to uncover if 2 triangles are congruent: SSS, SAS, ASA, AAS and also HL.

You are watching: A triangle with all sides congruent

1. SSS (side, side, side)

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SSS means "side, side, side" and means that we have two triangles through all three sides equal.

For example:

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is congruent to:
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(See resolving SSS triangles to uncover out more)


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


2. SAS (side, angle, side)

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SAS stands for "side, angle, side" and method that we have two triangles where we recognize two sides and also the had angle are equal.

For example:

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is congruent to:
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(See resolving SAS triangles to find out more)


If two sides and also the contained angle the one triangle room equal come the corresponding sides and also angle of an additional triangle, the triangles room congruent.


3. ASA (angle, side, angle)

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ASA means "angle, side, angle" and method that we have actually two triangles wherein we know two angles and the consisted of side space equal.

For example:

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is congruent to:
*

(See resolving ASA triangles to uncover out more)


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


4. AAS (angle, angle, side)

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AAS represents "angle, angle, side" and method that we have actually two triangles wherein we understand two angles and the non-included side space equal.

For example:

*
is congruent to:
*

(See addressing AAS triangle to uncover out more)


If two angles and also the non-included next of one triangle space equal to the corresponding angles and also side of one more triangle, the triangles room congruent.


5. HL (hypotenuse, leg)

This one uses only to best angled-triangles!

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or
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HL represents "Hypotenuse, Leg" (the longest next of a right-angled triangle is dubbed the "hypotenuse", the various other two political parties are dubbed "legs")

It way we have actually two right-angled triangle with

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

It doesn"t issue which leg because the triangles can be rotated.

For example:

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


If the hypotenuse and also one foot of one right-angled triangle room equal come the corresponding hypotenuse and also leg of one more right-angled triangle, the two triangles room congruent.


Caution! Don"t use "AAA"

AAA method we are provided all 3 angles of a triangle, yet no sides.

See more: Analysis Of The Song " Testify Lyrics Rage Against The Machine Meaning

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This is not sufficient information to decision if 2 triangles are congruent!

Because the triangles deserve to have the same angles yet be different sizes:

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is not congruent to:
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Without learning at the very least one side, us can"t be certain if 2 triangles are congruent.


Congruent Congruent Triangles comparable Similar triangles Finding similar Triangles Trigonometry table of contents