Congruence

 

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

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.

 

Reflection

Flipping

Translation

Sliding

Rotation

Turning

Congruence due to Same Sides

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

For Example:

is congruent to:

 

 

and

 

all three triangles have exactly the same sides.

But:

is NOT congruent to:

 

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

Congruence due to Same Angles

Two triangles with the same angles might be congruent:

is congruent to:

Since  they are the same size and same angles

But they might NOT be congruent because of different sizes:

is NOT congruent to:

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

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

 

is congruent to:

 

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.