Euclidean Geometry Flashcards
Theorem 1: If two triangles are equiangular
Corresponding sides are in prop
:. Two triangles are similar
R.T.P ab/de=bc/ef=ac/df
Theorem 1: How to prove ab/de=bc/ef=ac/df with two similar triangles
Congruency: Construction line so that sides equal T3=-T2
Sides in prop: Corresponding angl =, Parallel line divides sides in prop,
Theorem 2: Converse of first
If corresponding sides in prop then triangles are equiangular
Congruency
Areas of triangles: triangles share common vertex
Triangles with common height (traingles with common height)
:. Ratio of their areas=ratio of their bases (triangles w/ same height)
Theorem 3: Triangles with equal and common bases, lying between parallel lines
Same area
Triangles with same area
Theorem 5: Triangles w/ same angle and one adj side that is common
Ratio of their areas=ratio of other adj sides to the angle
Triangles w/ common angle
Theorem 6: Triangles between parallel lines
Ratio of the areas= ratio of their bases
Heights equal
(Triangles between the same parallel lines)
Theorem 7: Triangles with same bases and lie between parallel lines
Areas equal
Triangles between same parallel lines
PROP INT THEOREM
A straight line drawn parallel the one side of a triangle, divides the other two sides (or those sides produced) proportionally.
4 construct (between parallel lines and from parallel line to triangle) Triangles with same height, triangles between same parallel lines, common area w/ sub
PROP INT THEOREM CONVERSE
Proving parallel lines
If a straight line is drawn proportionally between two sides of a triangle, then the line will be parallel to the third side
“Parallel” Construction from line to side of traingle, prop int, equate, prove
Theorem 4: Triangles with equal height or same height
Ratio of their areas =ratio of their bases
THEROREM OF PYTHAG
(Perp drawn from right angled vertex)
All triangles similar to each other
X^2= Y.Z (in each triangle)
