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Euclidean Geometry Flashcards

(12 cards)

1
Q

Theorem 1: If two triangles are equiangular

A

Corresponding sides are in prop
:. Two triangles are similar
R.T.P ab/de=bc/ef=ac/df

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2
Q

Theorem 1: How to prove ab/de=bc/ef=ac/df with two similar triangles

A

Congruency: Construction line so that sides equal T3=-T2

Sides in prop: Corresponding angl =, Parallel line divides sides in prop,

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3
Q

Theorem 2: Converse of first

A

If corresponding sides in prop then triangles are equiangular
Congruency

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4
Q

Areas of triangles: triangles share common vertex

A

Triangles with common height (traingles with common height)

:. Ratio of their areas=ratio of their bases (triangles w/ same height)

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5
Q

Theorem 3: Triangles with equal and common bases, lying between parallel lines

A

Same area

Triangles with same area

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6
Q

Theorem 5: Triangles w/ same angle and one adj side that is common

A

Ratio of their areas=ratio of other adj sides to the angle

Triangles w/ common angle

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7
Q

Theorem 6: Triangles between parallel lines

A

Ratio of the areas= ratio of their bases
Heights equal
(Triangles between the same parallel lines)

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8
Q

Theorem 7: Triangles with same bases and lie between parallel lines

A

Areas equal

Triangles between same parallel lines

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9
Q

PROP INT THEOREM

A

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
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10
Q

PROP INT THEOREM CONVERSE

Proving parallel lines

A

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

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11
Q

Theorem 4: Triangles with equal height or same height

A

Ratio of their areas =ratio of their bases

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12
Q

THEROREM OF PYTHAG

A

(Perp drawn from right angled vertex)
All triangles similar to each other
X^2= Y.Z (in each triangle)

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