Congruent Triangles

Triangles are congruent when they have
exactly the same three sides and exactly the same three angles.

What is "Congruent" ... ?

It means that one shape can become another using Turns, Flips and/or Slides:

Rotation a Turn!
Reflection a Flip!
Translation a Slide!

(see Congruent for more info)

Congruent Triangles

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

Same Sides

When the sides are the same then the triangles are congruent.

For example:

triangle is congruent to:   triangle   and   triangle

because they all have exactly the same sides.

But:

triangle is NOT congruent to:   triangle

because the two triangles do not have exactly the same sides.

 

Same Angles

Does this also work with angles? Not always!

Two triangles with the same angles might be congruent:

triangle is congruent to: triangle

only because they are the same size

But they might NOT be congruent because of different sizes:

triangle is NOT congruent to: triangle

because, even though all angles match, one is larger than the other.

So just having the same angles is no guarantee they are congruent.

 

Other Combinations

There are other combinations of sides and angles that can work ...
... read more at How To Find if Triangles are Congruent

Marking

When two triangles are congruent we often mark corresponding sides and angles like this:

triangle is congruent to: triangle

The sides marked with one line are equal in length. Similarly for the sides marked with two lines. Also for the sides marked with three lines.

The angles marked with one arc are equal in size. Similarly for the angles marked with two arcs. Also for the angles marked with three arcs.