Chapter 7 Flashcards
Extended Ratios
comparison of 3 or more quantities
proportion
an equation stating that 2 ratios are equal
Cross Product Property
product of extremes=product of means
Geometric Mean
a/x=x/b
Arithmetic Mean
average of 2 numbers
2 polygons are similar if….
angles are congruent
sides are proportional
scale factor
ratio of lengths of corresponding sides of 2 similar polygons
Perimeters of similar polygons
proportional to scale factor
Areas of similar polygons
if scale factor is a/b, area is a^2/b^2
Angle Angle (AA) ~
if two angles of one triangle are similar to two angles of another, the triangles are similar
Side Side Side ~
If three sides of a triangle are proportional to 3 sides of another, the triangles are proportional
Side Angle Side ~
If two sides are proportional and one angle is congruent to two sides and one angle of another triangle, the triangles are congruent
midsegment
a segment connecting the midpoints of 2 sides of a triangle
Triangle Midsegment Theorem
A midsegment of a triangle is parallel to one side of the triangle, and the length is one half of the length of that side
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other two aides, then it divides the segments into segments of proportional length
Converse of Triangle Proportionality Theorem
If a line intersects two sides of a triangle into proportional segments, the line is parallel to the 3rd side of a triangle
Congruent Parts of Parallel Lines
If 3 or more parallel lines cut off congruent segments on one transversal, they cut off congruent segments at every transversal
Proportional Parts of Parallel Lines
If 3 or more Parallel lines intersect 2 transversals, then they cut off the transversal proportionally
Ratio
a quotient of two numbers, or comparison of 2 values
