Geometry Chapter 7 Flashcards
Principle 7: A line parallel to a side of a triangle cuts off a triangle…
similar to the given triangle.
If DE is parallel to BC then triangle ADE is similar to triangle ABC
Addition method
A proportion may be changed into an equivalent proportion by adding terms in each ratio to obtain new first and third terms.
If any three terms of one proportion equal the corresponding three terms of another proportion…
ther remaining terms are equal.
If the product of two numbers equals the product of two other numbers,
either pair may be made the means of a proportion and the other pair may be made the extremes.
if 3x=5y, then x:y=5:3 or y:x=3:5 or 3:y=5:x or 5:x=3:y
the length of the leg opposite the 60 degree angle equals
one half the length of the hypotenuse times the square root of 3.
b=1/2c*squareroot of 3
Principle 6: Two right triangles are similar if an accute angle…
of one is congruent to an acute angle of the other.
three or more parallel lines divide…
any two transversals proportionately.
If AB, EF, and CD are all parallel, then a/b=c/d
Principle 2: Corresponding sides of similar triangles are…
In proportion
if c^2 > a^2 + b^2 where c is the longest side of the triangle
then the triangle is an obtuse triangle.
11^2 > 6^2 + 8^2
hence triangle ABC is an obtuse triangle
Corresponding altitudes of similar triangles have…
the same ratio as any two corresponding medians
if triangle ABC is similar to triangle A’B’C’ then h/h’=m/m’
Perimeters of similar polygons have the same ratio as…
any two corresponding sides.
If quadrilateral I is similar to quadrilateral I’ then 34/17=4/2=6/3=10/5=14/7
Inversion method
A proportion may be changed into an equivalent proportion by inverting each ratio.
Corresponding segments of similar triangles are…
in proportion
Eight Arrangements of Any Proportion: Direction Down
Corresponding sides of similar triangles are…
in proportion
In a right triangle, the length of either leg is the mean proportional between…
the length of the hypotenuse and the length of the projection of that leg on the hypotenuse.
AB/BC=BC/BD and AB/AC=AC/AD
The fourth term of a proportion is the…
fourth proportional to the other three taken in order.
2:3=4:x, x is the fourth proportional to 2,3, and 4.
Principle 1: Corresponding angles of similar triangles…
are congruent
If a tangent and a secant intersect outside a circle…
the tangent is the mean proportional between the secant and its external segment
If PA is a tangent, then AB/AP=AP/AC
a 30degree-60degree-90degree triangle is one half…
an equilateral triangle
a = 1/2c. Consider that c=2; then a=1 and the pythagorean theorem gives
b^2 = c^2 - a^2 = 2^2 - 1^2 = 3 or b=square root of 3
Means of a proportion
The middle terms, that is, its second and third terms.
in a:b=c:d , the means are b and c
A 45-45-90degree triangle is one half…
a square.
c^2 = a^2 + a^2 or c = a square root of 2
the ratio of the sides is a:a:c = 1:1: square root of 2
Similar Polygons
Polygons whose corresponding angles are congruent and whose corresponding sides are in proportion. Similar polygons have the same shape although not necessarily the same size.
Eight Arrangements of Any Proportion
Direction Left
