1.1.1.1 Definition: Triangles are congruent if all
three sides in one triangle are congruent
to the corresponding sides in the other.
1.1.1.2 In the figure on the above, the two triangles have
all three corresponding sides equal in length
and so are still congruent, even though one is
the mirror image of the other and rotated.
1.1.2 SAS(Side-Angle-Side)
1.1.2.1 Definition: Triangles are congruent if any
pair of corresponding sides and their
included angles are equal in both triangles.
1.1.3 ASA(Angle-Side-Angle)
1.1.3.1 Definition: Triangles are congruent if any
two angles and their included side are
equal in both triangles
1.1.4 RHS(Right angle-Hypotenuse-Side)
1.1.4.1 Definition: Two right angled triangles are congruent if
the hypotenuse( longest part of a right angled triangle)
and the same length for one of the sides
1.2 Definition: Triangles are congruent when all corresponding sides
and interior angles are congruent. The triangles have the same
shape and size, but one may be a mirror image of the other or how
you rotate or move it around
2 Similarity
2.1 Conditions
2.1.1 SSS(Side-Side-Side)
2.1.1.1 Definition: Triangles are similar if all three sides in one
triangle are in the same proportion to the corresponding
sides in the other.
2.1.2 SAS(Side-Angle-Side)
2.1.2.1 Definition: Triangles are similar if
two sides in one triangle are in the
same proportion to the
corresponding sides in the other,
and the included angle are equal
2.1.3 AA(Angle-Angle)
2.1.3.1 Definition: Triangles are similar if the measure of all three interior
angles in one triangle are the same as the corresponding angles
in the other.
2.2 Definition: Triangles are similar if they have the same
shape, but different sizes. (They are still similar even if
one is rotated, or one is a mirror image of the other).