Ratio- comparison of two amounts
Proportions- statement of tow equivilent ratios, to solve use cross products
Properties of Proportions
a/b=c/d
1. ad=bc
2. b/a=d/c
3. a/c=b/d
4. a+b/b=c+d/d
Similar Polygons
1. Corresponding <'s are congruent
2. Corresponding sides are proportional
the ratio of the lengths of corresponding sides is the similarity ratio a/b
Section10-2
Proving triangles similar using AA, SAS, SSS
Postulate 10-1 angle angle similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles aren't similar
Theorem 10-1 side angle side similarity (SAS): If an angle of one triangle is congruent to the angle of a second triangle and the sides including the two angles are proportional, then the triangles are similar
Theorem 10-2 side side side similarity (SSS): If the corresponding sides of two triangles are proportional, then the triangles are similar
Section 10-3
Similarity in Right Rriangles
Theorem 10-3: The altitude to the hypotenuse of a
right triangle divides the triangle into two triangles that are similar to the original triangle and each other
Geometric mean- the geometric mean of A and B is A/x=x/B where A and B are both positive numbers
Section 10-4
Proportions and Similar Triangles
Theorem 10-4 side splitter: If a line is parallel to One side of a triangle and intersects the other Two sides, then it divides those sides proportionally
Corollary to Theorem 10-4: If three parallel linesintersect two transversals, then the segments intersepted on the transversals are porportional
Theorem 10-5 trianlge angle bisector: Ff a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle
Section 10-5/10-6
Perimeter, Area and Aolume
Perimeter= units a/b
Area= units squared Asquared/Bsquared
Volume= units cubed Acubed/Bcubed
