exactly the exact same three sides and also specifically the very same three angles.

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

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

You are watching: What else must you know to prove the triangles congruent by asa? by sas?

## 1. SSS (side, side, side) SSS means "side, side, side" and means that we have actually two triangles with all three sides equal.

For example: is congruent to: (See fixing SSS triangles to discover out more)

If three sides of one triangle are equal to three sides of an additional triangle, the triangles room congruent.

## 2. SAS (side, angle, side) SAS stands for "side, angle, side" and way that we have actually two triangles where we recognize two sides and the had angle space equal.

For example: is congruent to: (See solving SAS triangle to discover out more)

If 2 sides and the contained angle the one triangle space equal to the equivalent sides and angle of another triangle, the triangles are congruent.

## 3. ASA (angle, side, angle) ASA represents "angle, side, angle" and method that we have two triangles whereby we know two angles and also the consisted of side space equal.

For example: is congruent to: (See solving ASA triangles to uncover out more)

If 2 angles and also the included side the one triangle are equal to the corresponding angles and side of one more triangle, the triangles room congruent.

## 4. AAS (angle, angle, side) AAS stands for "angle, angle, side" and method that we have two triangles where we know two angles and the non-included side room equal.

For example: is congruent to: (See resolving AAS triangles to find out more)

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

## 5. HL (hypotenuse, leg)

This one applies only to ideal angled-triangles! or HL represents "Hypotenuse, Leg" (the longest next of a right-angled triangle is called the "hypotenuse", the other two sides are referred to as "legs")

It method we have two right-angled triangles with

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

It doesn"t issue which leg since the triangles could be rotated.

For example: is congruent to: (See Pythagoras" theorem to uncover out more)

If the hypotenuse and also one foot of one right-angled triangle space equal come the corresponding hypotenuse and also leg of one more right-angled triangle, the 2 triangles space congruent.

## Caution! Don"t use "AAA"

AAA method we are given all 3 angles the a triangle, but no sides.

See more: Northern Renaissance Art Vs Italian Renaissance Art By, Access Denied This is not sufficient information to decide if two triangles room congruent!

Because the triangles have the right to have the exact same angles but be different sizes: is not congruent to: Without learning at the very least one side, we can"t be certain if 2 triangles are congruent.

Congruent Congruent Triangles similar Similar triangle Finding comparable Triangles Trigonometry index