Chapter 7 Flashcards
A comparison of two quantities
Ratio
A/b is equal to ad=BC, b/a=d/c,a+b/b=c+d,
Properties of proportions
A statement that two ratios are equal
Proportion
When tree or more ratios are equal
Extended proportion
If u multiply both sides of a/b = c/d by b then the product of the extreme is = to the product of the means
Cross product property
A drawing in which all lengths are proportional to corresponding actual lengths
Scale drawing
The ratio of any length in a scale drawing to the corresponding actually length the length may be in different units
Scale
Have corresponding naked and corresponding sides proportional
Similar figures
Ratio of the lengths of corresponding sides
The similarity ratio
A rectangle that can be divided into a square and a rectangle that is similar to the original rectangle
Golden rectangle
1.618:1
Golden ratio
Two angles of one triangle are congruent to two angles of another triangle then the triangles are similar
Angle-Angle similarity
If one angle of one triangle is similar to an angle of a second triangle and the sides including the angle are proportional then the triangles are similar
Side angle side similarity
If the corresponding sides of two triangles are proportional then the triangle are similar
Side side side similarity
A way of measuring things that are difficult to measure directly
Indirect measurement
The altitude to the hypotenuse of a right triangle divides the triangles into two triangles that are similar to the original triangle are to each other
Theorem 7-3
The 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 1 to theorem 7-3
The altitude of the hypotenuse of the right triangle separates the hypotenuse so that the length of each leg of the triangles is the geometric mean of the length of the other adjacent hypotenuse segment and the length of the hypotenuse
Corollary 2 to theorem 7-3
Two positive numbers A and B is the positive number x such that a/x = x/b
Geometric mean
If a line is parallel to one side of a triangle and intersects the other two sides then it divides those sides proportionally
Side splitter theorem
Of three parallel lines intersect two transversals then the segments intercepted on the transversals are proportional
Corollary to theorem 7-4
If a ray bisects an angle of a triangle then it divides the opposite sed into two segments that are proportional to the other two sides of the triangle
Triangle angle bisector theorem
