Ch. 8 Vocab And Theorems Flashcards
(17 cards)
Proportion
A comparison of two ratios
Ratio
A comparison of two quantities
Properties of proportions
a/b = c/d is equivalent to
(1) ad = bc
(2) b/a = d/c
(3) a/c = b/d
(4) a+b/b = c+d/d
Similar polygon
(1) Corresponding angles are congruent
(2) Corresponding sides are proportional
Similarity ratio
The ratio of the lengths of corresponding sides of similar polygons.
Golden rectangle
A rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.
Golden ratio
About 1.618
AA~ Pos
if two corr angles are congruent then similar
SAS~ Thm
Angle congruent and included sides proportional then similar
SSS~ Thm
Corr sides proportional the similar
Altitude to Hypotenuse Theorem
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and each other.
Geometric mean
a/x = b/x x = square root ab
Corollary 1 to Altitude to Hypotenuse Theorem
Then length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse
Corollary 2 to Altitude Hypotenuse Theorem
The altitude of the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.
Side-Splitter Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
Corollary to the Side-Splitter Theorem
If three parallel lines intersect two transversals, the. The segments intercepted on the transversals are proportional.
Triangle-Angle-Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
