Geometry: Triangles

Sum of the angles

The sum of the angles of a triangle is 180o

Exterior angles

If one side of a triangle is produced, the exterior angle formed is equal to the sum of the opposite interior angles

Equal Sides

If two sides of a triangle are equal, the angles opposite them are equal

Equal Angles

If two angles of a triangle are equal, the sides opposite them are equal

Congruent Triangles

Two triangles are congruent if they have the same shape and size (corresponding angles are equal, and corresponding sides are equal)

Congruent Triangles:SSS

SSS: If the three sides of a triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent

Congruent Triangles:SAS

SAS:If two sides and the included angle of a triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent

Congruent Triangles:AAS

AAS:If two angles and a side of a triangle are equal to the two angles and the corresponding side of another triangle, then the two triangles are congruent

Mid-Point Theorem

The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half of it in length

The line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side

Similar Triangles

Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional

Areas of similar triangles are proportional to the squares on corresponding sides