specifically the very same 3 sides and precisely the same three angles.

But we don"t need to understand all three sides and also all 3 angles ...normally three out of the six is sufficient.

Tbelow are five means to find if two triangles are congruent: SSS, SAS, ASA, AAS and also HL.

You are watching: What other information do you need in order to prove the triangles congruent using the sas

1. SSS (side, side, side)

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SSS means "side, side, side" and also implies that we have two triangles through all 3 sides equal.

For example:

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is congruent to:
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(See Solving SSS Triangles to find out more)


If three sides of one triangle are 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 suggests that we have two triangles wright here we understand 2 sides and also the consisted of angle are equal.

For example:

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is congruent to:
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(See Solving SAS Triangles to uncover out more)


If 2 sides and also the included angle of one triangle are equal to the matching sides and also angle of another triangle, the triangles are congruent.


3. ASA (angle, side, angle)

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ASA means "angle, side, angle" and also indicates that we have actually two triangles wbelow we know 2 angles and also the consisted of side are equal.

For example:

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is congruent to:
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(See Solving ASA Triangles to uncover out more)


If 2 angles and also the contained side of one triangle are equal to the matching angles and side of another triangle, the triangles are congruent.


4. AAS (angle, angle, side)

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AAS stands for "angle, angle, side" and also indicates that we have actually 2 triangles wright here we recognize 2 angles and the non-contained side are equal.

For example:

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is congruent to:
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(See Solving AAS Triangles to discover out more)


If 2 angles and also the non-had side of one triangle are equal to the equivalent angles and side of an additional triangle, the triangles are congruent.


5. HL (hypotenusage, leg)

This one applies only to appropriate angled-triangles!

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or
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HL stands for "Hypotenusage, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other 2 sides are dubbed "legs")

It suggests we have actually two right-angled triangles with

the exact same size of hypotenuse and the exact same length for one of the various other 2 legs.

It doesn"t matter which leg considering that the triangles might be rotated.

For example:

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is congruent to:
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(See Pythagoras" Theorem to discover out more)


If the hypotenusage and also one leg of one right-angled triangle are equal to the matching hypotenusage and also leg of an additional right-angled triangle, the two triangles are congruent.


Caution! Don"t Use "AAA"

AAA indicates we are provided all three angles of a triangle, but no sides.

See more: 10000*.08 - 10 Per Bag

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This is not enough information to decide if 2 triangles are congruent!

Due to the fact that the triangles can have actually the very same angles however be different sizes:

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is not congruent to:
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Without discovering at leastern one side, we can"t be sure if two triangles are congruent.


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