Triangle ABC, D in AB, E in AC, DE//BC <=> AD/AB=AE/AC=DE/BC and triangle ABC is similar to triangle ADE
Euclide Geometry Principles
Central symmetry of triangle ABC AB=A’B’, BC=B’C’, AC=A’C’ ∠ABC= ∠A’B’C’, ∠BAC=∠B’A’C’, ∠ACB= ∠A’C’B’ AB//A’B’, BC//B’C’, AC//A’C’ See also « Isometric transformation«
Isometric transformation – Central symmetry
Axial symmetry of triangle ABC AB=A’B’, BC=B’C’, AC=A’C’ ∠ABC= ∠A’B’C’, ∠BAC=∠B’A’C’, ∠ACB= ∠A’C’B’ See also « Isometric transformation«
Isometric transformation – Axial Symmetry
Displacement of Triangle ABC AB=A’B’, BC=B’C’, AC=A’C’ ∠ABC= ∠A’B’C’, ∠BAC=∠B’A’C’, ∠ACB= ∠A’C’B’ See also « Isometric transformation«
Isometric transformation – Displacement
Rotation of triangle ABC from point O with angle α AB=A’B’, BC=B’C’, AC=A’C’ ∠ABC= ∠A’B’C’, ∠BAC=∠B’A’C’, ∠ACB= ∠A’C’B’ ∠(AB,A’B’)=∠(AC,A’C’)=∠(BC,B’C’)=α See also « Isometric transformation«
Isometric transformation – Rotation
To solve a problem, it could be necessary to add one or more points.
Additional points
Isometric transformation and combinations of Isometric transformation preserve angles and distances: displacement rotation axial symmetry central symmetry
Isometric transformation
The quadrilateral ABCD is a parallelogram <=> Two pairs of opposite sides are parallel <=> Two pairs of opposite sides are equal <=> Two pairs of opposite angles are equal <=> Adjacent angles are supplementary <=> The diagonals bisect each other <=> One pair of opposite sides is parallel and […]
Parallelogram
Equilateral triangle <=> AB=AC=BC ∠CAB=∠ABC=∠BCA=Π/3=60°
Equilateral triangle
Triangles are congruent <=> they have exactly the same three sides they have exactly the same three angles they have exactly the same two angles (the third angle is deducted)