Download 8 - Angelfire

Ratio: (Page 282) A comparison of two quantities
a
b
Proportion: (Page 283) Equivalent fractions set equal to each other.
a = c
b
d
Cross Products: (page 283) Cross Multiplication:
Extremes/Means: (pages 283) 3 = 6
8
4
3= 6
4
x
Chapter 6 & 7 Vocabulary
Similar Polygons: Polygons with the same shape but different in size
are proportional. (Page 289)
A
B
E
F
4
D
C
8
8
G
H
16
AD = EH
CD
GH
64 = 64
4 = 8
16
8
Scale Factor: The ratio resulting in the comparison of two lengths
4 =
8
… a scale factor of 1 (we simply reduce)
2
Chapter 6 & 7 Vocabulary
Angle Angle (AA) Postulate: If two angles of 2 triangles are
congruent, then the triangles are
similar. (Page 298)
3rd Angle Theorem and Angle Sum Theorem
Chapter 6 & 7 Vocabulary
SSS Similarity: If the measures of the corresponding sides of
2 triangles are proportional, then the triangles
are similar. (Page 299)
5
3
10
6
4
3 = 6
4
8
3 = 4
6
8
8
Chapter 6 & 7 Vocabulary
SAS Similarity:
If the measures of 2 sides of a triangle are proportional to 2 sides
of another triangle, and the included angles are congruent, then the
triangles are similar. (Page 299)
5
10
4
4 = 8
5
10
8
Chapter 6 & 7 Vocabulary
Triangle Proportionality Theorem and it’s Converse:
A line parallel to another side of a triangle intersecting the same
triangle separates the triangle into proportional segments.
(Page 307, 308)
10
6
8
3
3 = 5
3
5
5
5
3
8
Chapter 6 & 7 Vocabulary
D Mid-segment Theorem: (Page 308)
A mid-segment of a triangle is parallel to one side of said triangle
and has a length half that of the side to which it is parallel.
10
6
6
10
8
16
Chapter 6 & 7 Vocabulary
Proportional Perimeters Theorem:
If 2 triangles are similar, then the measures of their perimeters are
proportional to the measures of the corresponding sides. (Page 316)
10
6
8
5
3
4
6 = 3
24
12
72 = 72
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #1:
If 2 triangles are similar, then the measures of their corresponding
altitudes are proportional to the measures of their corresponding sides.
(Page 317)
=
6=6
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #2:
If 2 triangles are similar, then the measures of their corresponding
angle bisectors are proportional to the measures of their corresponding
sides. (Page 317)
A
B
C
D
E
AD = AB
EH
EF
F
H
G
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #3:
If 2 triangles are similar, then the measures of their corresponding
medians are proportional to the measures of their corresponding
sides. (Page 317)
A
B
C
D
E
AD = AC
EH
EG
F
H
G
Chapter 6 & 7 Vocabulary
Iteration: Repeating the same process over and over again.
(Page 317)
Chapter 6 & 7 Vocabulary
Fractal: A Geometric figure that is created using iteration.
(Page 325)
Chapter 6 & 7 Vocabulary
Self Similar: Where we observe smaller portions of a shape or
figure to possess the same geometric characteristics
as the original figure.
(Page 325)
Chapter 6 & 7 Vocabulary
Pythagorean Theorem: a2 + b2 = c2 (Page 350)
Pythagorean Triple: (Page 352)
Justification:
3
4
5
5
12 13
9 + 16 = 25
25 + 144 = 169
4+4=8
(45-45-90)
4 + 12 = 16
(30-60-90)