Chapter 7 Flashcards
B. d
Properties of proportions
Comparison of two quantities
Ratios
Compared each length in a drawing to the actual length
The scale
Two figures that have the same shape but not necessarily the same size are
Similar
The ratio of lengths of corresponding sides
Similarity ratio
Rectangle that can be duvided into a square and a rectangle that is similar to the original rectangle
Golden rectangle
1.618:1
Golden ratio
If two angles of one triangle are congruent to two angles of another triangle then the triangle are similar
AA~
If an angle of one triangle is congruent a to the angle of another, and the sides including the angles are proportional then the triangles are similar
Side angle side~
If the corresponding sides of two triangles are proportional then the triangles are similar
SSS~
The altitude to the hypotenuse if a right triangle divides the triangle into two other triangles that are similar to the original triangle and to each other
7-3
For any two positive numbers a and b , a/x=x/b
Geometric mean
The length of the altitude to the hypotenuse of a right triangleis the geometric mean of the lengths of the segments of the hypotenuse
Corallary 1 7-3
The altitude to the hypotenuse of a right triangle seperates 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
Corallary 2 7-3
If a line is parrallel to one side of a triangle and intersects the other two sides then it divides those sides proportionally
Side splitter theorem
If three parallel lines intersect two transversals then the segments intercepted on the transversals are proportional
Corallary to 7-4
If a ray bisects am angle of a triangle them it divides the opposite side into two segments that are proportional to the other two sides of the triangle
Triangle angle bisector theorem
