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Geometry Unit 5 - Similar Triangles
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Terms in this set (25)
ratio
comparison of two numbers measured in the
same units
rate
ratio with different units
extended ratio
a ratio with more than two numbers
proportion
equation of two equal ratios
means
the denominator of the first ratio and the numerator of the second ratio in a proportion
extremes
the numerator of the first ratio and the denominator of the second ratio in a proportion
cross product property
the product of the means equals the product of the extremes
reciporical property
the reciprocals of the ratios in a proportion are also equal to each other
switched means
two ratios in a proportion are still equal to each other if the means are switched
switched extremes
two ratios in a proportion are still equal to each other if the extremes are switched
adding denominator to numerator
two ratios in a proportion are still equal to each other if the denominator of each ratio is added to the numerator of that ratio
similar polygons
polygons with congruent angles and proportional sides
scale factor
the ratio of the corresponding side lengths of two similar polygons
∼
similarity symbol
statement of proportionality
an extended ratio comparing two similary polygons
similarity statement
a statement saying two figures are similar
theorem 6.1
the ratio of the perimeter of two similar figures is equal to the scale factor
corresponding lengths in similar polygons
if two polygons are similar, then the ratio of any two corresponding lengths in the polygons is equal to the scale factor of the similar polygons.
similarity of congruent figures
congruent figures are always similar, but not all similar figures are congruent
congruent → similar
angle-angle similarity postulate (AA∼)
if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
side-side-side similarity postulate (SSS~)
if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar
side-angle-side similarity postulate (SAS~)
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
triangle proportionality theorem
if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally
three parallel lines theorem
if three parallel lines intersect two transversals, then they divide the two transversals proportionally
angle bisection
if a ray bisects an angle of a triangle, then it divides the opposite sides into segments whose lengths are proportional to the lengths of the other two sides
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