Geometry Chapter 7 Theorems and Postulates
Ratio
a comparison of two quantities by division
Golden Rectangle
a rectangle that can be divided into a square and a rectangle that is similar the the original rectangle
Proportion
a statement that two ratios are equal
Properties of Proportions
a/b=c/d is equivalent to a/c=b/d a/b=c/d is equivalent to d/b=c/a a/b=c/d is equivalent to b/a=d/c
Theorem 7-4: 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
Theorem 7-5: Triangle-Bisector Theorem
if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides
Theorem 7-2:Side-Angle-Side Similarity Postulate
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 the triangles are similar
Theorem 7-3: Side-Side-Side Similarity Postulate
if the corresponding sides of two triangles are proportional, then the triangles are similar
Corollary to Theorem 7-4
if three parallel lines intersect two transversal, then the segments intercepted on the transversal are proportional
Postulate 7-1:Angle-Angle Similarity Postulate
if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
Similar Polygons
polygons having corresponding angles congruent and corresponding sides proportional
Theorem 7-3
the altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other
Corollary to Theorem 7-3
the length of the altitude to the hypotenuse of a right triangle is the geometric means of the lengths of the segments of the hypotenuse
Geometric Mean
the number x such that a/x=x/b where a,b, and x are positive numbers
Cross-Product Property
the product of the extremes is equal to the product of the means
Scale
the ratio of any length in a scale drawing to the corresponding actual length
Golden Ratio
the ratio of the length of a golden rectangle to its width. about 1.62
Similarity Ratio
the ratio of the lengths of corresponding sides
