Geometry Ch. 10 Flashcards
ratio
comparing to parts in fraction form The ratio of a to b (a:b) is a/b
proportion
the equality of two ratios a/b = c/d or 1/2 = 3/6
Geometric mean
the number that is the same on both ratios a/b = b/c (b is the geometric mean)
1/2 = 2/4 (2 is the geometric mean)
similar
two polygons are similar if their corresponding angles are congruent (equal) and their corresponding sides are proportional
dilation
an enlargement or reduction of a shape so that the two shapes are similar and their corresponding vertices lie on the same rays emanating from a center point
magnitude r
the ratio of the corresponding sides of similar shapes which tells us by how much the original shape has been magnified or reduced.
Below, the magnitude of the large triangle compared to the small triangle is 2:1 or 2. The small triangle to the large triangle is 1/2. In other words, the small triangle is 1/2 the size of the large triangle.
center of a dilation
like a projector light when showing an image on the board or the concurrent point where the rays that transect the vertices of the dilation come together
Theorem 44- The Side Splitter Theorem:
if a parallel line is drawn through two sides of a triangle and parallel to the third side, then it divides those two sides at the same ratio
Theorem 45: AA Theorem-
If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar
Corollary to Theorem 45 AA Theorem
Two triangles similar to a third triangle are similar to each other
Theorem 46: Corresponding Altitudes of Similar Polygons-
corresponding altitudes of similar triangles have the same ratio as the corresponding sides
Theorem 47: Perimeters of Similar Polygons:
the ratio of the perimeters of two similar polygons is equal to the ratio of their corresponding sides
Theorem 48: Areas of Similar Polygons-
the ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding sides
