Chapter 7 Flashcards
definition of similar polygons
same shape, different size
two polygons are similar if they BOTH have:
- corresponding angles are congruent
2. corresponding sides are proportional
what is a similarity ratio?
the ratio of the lengths of corresponding sides
what is the similarity ratio also known as?
scale factor
Angle-Angle Similarity Theorem (AA ~)
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.
Side-Angle-Side Similarity Theorem (SAS ~)
If an ANGLE of one triangle is CONGRUENT to an angle of a second triangle, and the SIDES including the 2 angles are PROPORTIONAL, then the triangles are SIMILAR
Theorem 7-3 (altitude):
The altitude to the hypotenuse of a right triangle divides the triangle into TWO triangles that are SIMILAR to both the ORIGINAL triangle and to EACH OTHER
The length of the altitude to the hypotenuse is the GEOMETRIC MEAN between the SEGMENTS of the HYPOTENUSE
piece / alt = alt / piece
EACH LEG of the triangle is the GEOMETRIC MEAN between the LENGTH of the HYPOTENUSE and the ADJACENT SEGMENT of the HYPOTENUSE
hypotenuse / leg = leg / piece
multiplying radicals
multiply the radical part, simplify, the multiply the integers
dividing radicals
divide the radicals, simplify, and divide integers
ex: 2√6 / √3 = 2√2
rationalizing radicals
multiply by the radical, simplify
45-45-90 Triangle Theorem:
In a 45-45-90 triangle, both legs are congruent, and the length of the hypotenuse is radical 2 times the length of the leg
how to find the hypotenuse of a 45-45-90
√2 • leg
how to find the leg of a 45-45-90 triangle
√2
