Note card chapter 7
dilations - produces an image that is different size from its pre image
Ration method 1. Draw a ray from point p to each vertex of triangle
abc
2. Mark point a’ so that the point is half the distance from point p to a.
Repeat for b and c
3. Draw a segment connect A
Geometric mean a/x = x/b this is to find the altitude which
10/30=100/x =300
This isAA because both triangles have a right angle and share an
angle
Theorem 7.1: Angle-Angle (AA) Similarity:
If two angles of one triangle are congruent to two angles of another
triangle, then the triangles are similar
. <A
≅ <D and <B
≅ <E then
∆ABC~∆DEF
Theorem 7.2: Side-Side-Side (SSS) Similarity: If the corresponding
side lengths of two triangles are proportional, then the triangles are
similar∆ ABC~∆ DEF
Theorem 7.3: if an angle of one triangle is congruent to an angle of a
second triangle, and the sides that include the two angles are
proportional then the triangles are similar≅ <E and AB/DE
=BC/EF then ∆ABC~∆DEF
Theorem 7.4: 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
Theorem 7.5 if a line is parallel to one side of a triangle and intersects
the other two sides, then it divides those sides proportionally if
MNǁAC them AM/MB=CN/NB
Theorem 7.6: if a segment joins the midpoint of two sides of a
triangle, then the segment is parallel to the third side and is half as
long if DG≅ GE amd FH≅HE
Theorem 7.7: if a ray bisects an angle of a triangle the it divides the
opposite side into two segments such that the ratio between the
segments is the same as the ratio between the sides adjacent to
each segment if <UVX ≅ WVX then UX/WX=UV/WV
