Congruent Triangles Introduction
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:
(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 is Enough
When the sides are the same the triangles are congruent.
For example:
because they all have exactly the same sides.
But:
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:
only because they are the same size
But they might NOT be congruent because of different sizes:
all angles match, but one triangle 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:
- SAS meaning "side, angle, side"
- ASA meaning "angle, side, angle"
- AAS meaning "angle, angle, side"
- HL meaning "hypotenuse, leg" in a right-angled triangle
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:
The sides marked with one line are equal in length. Similarly for the sides marked with two lines and also those with three lines.
The angles marked with one arc are equal in size. Similarly for the angles marked with two arcs and also those marked with three arcs.