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Chapter 6 & 7 Vocabulary. a b. Ratio : (Page 282) A comparison of two quantities. Proportion : (Page 283) Equivalent fractions set equal to each other. a b. c d. =. 3 4. 6 x. Cross Products : (page 283) Cross Multiplication:. =. 6 8. 3 4. Extremes /. Means : (pages 283). =. - PowerPoint PPT Presentation
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Ratio: (Page 282) A comparison of two quantities ab
Proportion: (Page 283) Equivalent fractions set equal to each other. ab
cd
=
Cross Products: (page 283) Cross Multiplication: 34
= 6x
Extremes/Means: (pages 283) 34
= 68
Chapter 6 & 7 Vocabulary
Similar Polygons: Polygons with the same shape but different in size are proportional. (Page 289)
A B
CD
E F
GH
Scale Factor: The ratio resulting in the comparison of two lengths
48
48
= … a scale factor of 12
(we simply reduce)
ADCD
= EHGH
8
16
48
= 8 16
64 = 64
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)
3
4
5
6
8
10
34
= 6 8
36
= 4 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)
4
5
8
10
45
= 8 10
Chapter 6 & 7 Vocabulary
Triangle Proportionality Theorem and it’s Converse:
A line parallel to another side of a triangle intersecting the sametriangle separates the triangle into proportional segments. (Page 307, 308)
8
106
8
53
3 5
33
= 5 5
Mid-segment Theorem: (Page 308)
A mid-segment of a triangle is parallel to one side of said triangleand has a length half that of the side to which it is parallel.
16
106
6 108
Chapter 6 & 7 Vocabulary
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)
8
106
53
624
= 3 12
472 = 72
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #1:
If 2 triangles are similar, then the measures of their correspondingaltitudes 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 correspondingangle bisectors are proportional to the measures of their correspondingsides. (Page 317) A
CBD
E
GFH
ADEH
= ABEF
Chapter 6 & 7 Vocabulary
Similar Triangle Theorem #3:
If 2 triangles are similar, then the measures of their correspondingmedians are proportional to the measures of their correspondingsides. (Page 317) A
CBD
E
GFH
ADEH
= ACEG
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)
3 4 5
5 12 13
Justification:
9 + 16 = 25
25 + 144 = 169
4 + 4 = 8
4 + 12 = 16
(45-45-90)
(30-60-90)
