Chapter 8 Flashcards
Note #1
Ratios are always in simplest form.
Ratio
Comparison of two numbers using division.
Notes #2
Ratios must compare the same units
Note #3
a to b doesn’t equal b to a (generally)
Proportion
Equation stating that two ratios are equal.
Cross-Product
If a/b=c/d, then a•d=b•c
Reciprocal Property
If a/b=c/d, then b/a=d/c
Interchange Means Property
If a/b=c/d, then a/c=b/d
Geometric Means
The geometric mean of 2 numbers a and b is the positive number x such that a/x=x/b
Nameless Property
A/b=c/d if and only if a+b/b=c+d/d
Similar Polygons
Two polygons are similar if
- ) Their corresponding angles are congruent
- ) The lengths of corresponding sides are proportional
Scale Factor
Common Ratio of 1/2 or 1:2
Theorem 8.1
If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides.
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
SSS Similarity Theorem
If corresponding sides of two of two triangles are proportional, then the two triangles are similar.
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then these triangles are similar.
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the 2 sides proportionally.
Triangle Proportionality Converse
If a line divides 2 sides of a triangle proportionally, then it is parallel to the 3rd side.
Theorem 8.6
If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally
Theorem 8.7
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other 2 sides.
