triangle similarity defns Flashcards
if the corresponding angles and sides of two triangles are respectively congruent and proportional, the two triangles are
similar
what do you call the side of a right triangle that forms the reference angle
adjacent
“if a line intersects any two sides, and is parallel to the third side, it divides the two sides proportionally”
the basic proportionality theorem
“If two triangles have 2 pairs of congruent corresponding angles, then the 3rd pair of corresponding angles are also congruent”
corollary to the triangle sum theorem
“If a line intersects two sides of a triangle and cuts off segments proportional to these two sides, then it is parallel to the third side
Converse of Basic Proportionality Theorem
bonus
bonus
“If two pairs of corresponding sides are proportional and included angles are congruent, then correspondence is a similarity”
SAS Similarity theorem
“If corresponding sides are proportional, then the correspondence is a similarity.”
SSS Similarity Theorem
“If corresponding angles are congruent, then the correspondence is a similarity”
AAA Similarity Theorem
“If two pairs of corresponding angles are congruent, then the congruence is a similarity”
AA Corollary
“The segment between the midpoints of two sides of a triangle is parallel to the third side and half as long”
The Midline Theorem
“An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the two other sides”
Angle Bisector Proportionality Theorem
“In any right triangle, the altitude to the hypotenuse separates the triangle into 2 triangles which are similar to each other & to the original triangle”
Right Triangle Similarity Theorem
The positive number x that satisfies a/x = x/b is the geometric mean of two positive numbers a & b
Geometric Mean Definition
