Download Chapter 1: Tools of Geometry

Theorem 8-5: Triangle-Angle-Bisector Theorem
If 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.
Chapter 8: Similarity
Postulate 8-1: Angle-Angle Similarity (AA ~) Postulate
If two angles of one triangle are congruent to two angles of
another triangle, then the triangles are similar.
Theorem 8-1: Side-Angle-Side Similarity (SAS ~) Thm
Theorem 8-6: Perimeters and Areas of Similar Figures
a
If the similarity ratio of two similar figures is , then
b
a
(1) the ratio of their perimeters is
and
b
a2
(2) the ratio of their areas is
b2
If an angle of one triangle is congruent to an angle of a second
triangle, and the sides including the two angles are
proportional, then the triangles are similar.
.
Theorem 8-2: Side-Side-Side Similarity (SSS ~) Theorem
If the corresponding sides of two triangles are proportional,
then the triangles are similar.
Theorem 8-3
Theorem 8-4: Side-Splitter Theorem
The altitude to the hypotenuse of a right triangle divides the
triangle into two triangles that are similar to the original triangle
and to each other.
If a line is parallel to one side of a triangle and intersects the
other two sides, then it divides those sides proportionally.
Corollary 1
Corollary
The length of the altitude to the hypotenuse of a right triangle is
the geometric mean of the lengths of the segments of the
hypotenuse.
If three parallel lines intersect two transversals, then the
segments intercepted on the transversals are proportional.
Converse
Corollary 2
The altitude to the hypotenuse of a right triangle separates the
hypotenuse in such a way that the length of each leg of the
triangle is the geometric mean of the length of the adjacent
hypotenuse segment and the length of the hypotenuse.
If a line divides two sides of a triangle proportionally, then it is
parallel to the third side.