Unit 13 Flashcards
Definition of similar polygons via measurement
Two polygons are considered similar if their corresponding angles are congruent (equal in measure) and their corresponding sides are proportional (in the same ratio)
Definition of similar via transformation
Two polygons if and only if one can be transformed into the other using a combination of rigid transformations and dilations
AA similarity postulate
If two angles of one triangle are congruent to two angles of another triangle then those triangles are similar
SAS similarity theorem
If an angle of one triangle is congruent to another triangle angle, and if the sides a re proportionate, then those triangles are similar
SSS similarity theorem
If all three sides have the same scale factor in a triangle then those triangles are simillar
Triangle proportionality theorem
If a line parallel to one side of a triangle intersects the other two side, then it divides those sides proportionally
Definiton of midsegment
A midsegment of a triangle is made if and only if its endpoints are the midpoints of two sides of the triangle
Midsegment theorem
If a segment of a triangle is a midsegment, then it is parallel to the base and half the distance of the base it is parallel with.
Triangle angle bisector theorem
in a triangle, an angle bisector divides the opposite side into two segments that are proportional to the lengths of the other two sides of the triangle
Three parallel lines theorem
If three parallel lines intersect two transversals, then they divide the transversal proportionally
Definition of geometric mean
Given 2 positive numbers a and b, a positive number x that satisfiess a/x = x/b, x_2 = ab, or x= sqrt ab is called the geometric mean of a and b
Right triangle similarity theorem
If the altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar to the original triangle and each other.
Geometric mean(leg) theorem
The length of the altitudes is the geometric mean of the length of the two segments of the hypotenuse
