unit 2: congruence, similarity, and proofs · vocabulary builder congruent statement angle measure...
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Unit 2: Congruence, Similarity, and Proofs
2.6 Similar Figures
2.6 Similar Figures
ratio= 0
proportion
equal𝒂𝒅 = 𝒄𝒅
𝟑
𝟒
𝟏
𝟕
𝟐
𝟑
16 4 24
2.6 Similar Figures
𝟒
𝟓
𝟏
𝟐
𝟒
𝟓
36 10
33
2.6 Similar Figures
similar shapesize
congruentproportional
𝟑
𝟔=𝟒
𝟖
𝒚𝒆𝒔
𝟐
𝟓𝒚𝒆𝒔
2.6 Similar Figures
𝟔
𝟏𝟐=
𝒙
𝟏𝟔x = 8
𝟔
𝟏𝟐=
𝒚
𝟐𝟎y = 10
𝟐𝟎
𝟑𝟎=𝟐𝟎
𝒙x = 30
𝟐𝟎
𝟑𝟎=𝟐𝟎
𝒚y = 30
2.6 Similar Figures
Similarity statement
Similarity ratio lengths
~
𝟖
𝟔=𝟒
𝟑15
9
2.6 Similar Figures
𝒙
𝟗=
𝟖
𝟏𝟐
x = 6𝟏𝟎
𝟓=𝟒. 𝟓
𝒙x = 2.25
𝟏𝟐
𝟏𝟖=𝒙 + 𝟏
𝟐𝟒x = 15
𝟒𝟎
𝟑𝟎=𝒙 + 𝟏𝟓
𝟏𝟖x = 9
2.6 Similar Figures
2.6 Similar Figures
2.6 Similar Figures
2.6 Similar Figures
BC = 10
Perimeter = 16 + 12 +10
Perimeter = 38
2.6 Similar Figures
2x - 6 = 𝟏
𝟐(𝟏𝟖)
x = 7.5
ED = 11.5
x = 6
2.6 Similar Figures
𝑨𝑬
𝑬𝑩=𝑨𝑭
𝑭𝑪
𝑬𝑭 ∥ 𝑩𝑪
2.6 Similar Figures
2.6 Similar Figures
2.6 Similar Figures
2.6 Similar Figures
𝑨𝑪
𝑪𝑬=𝑩𝑫
𝑫𝑭
2.6 Similar Figures
Unit 2: Congruence, Similarity, and Proofs
2.7 Similar Figures
2.7 Dilations and Similarity
dilation
Center of dilation
inside on outside
similar
Angle measure
length
proportional
multiply
Scale factor
enlargement
reduction
2.7 Dilations and Similarity
A
B
A’
B’
Scale Factor = −𝟐
−𝟒
𝑺. 𝑭.=𝟏
𝟐
Center of Dilation (0,0)
2.7 Dilations and Similarity
A
B C
A’
B’ C’
Scale Factor = −𝟕.𝟓
−𝟓
𝑺. 𝑭.=𝟑
𝟐= 𝟏. 𝟓
Center of Dilation (0,0)
2.7 Dilations and Similarity
Unit 2: Congruence, Similarity, & Proofs
Vocabulary Builder
Vocabulary Builder
Parallel Lines Alternate Exterior Angles Plane
Same-Side Interior Angles Skew Lines Corresponding Angles
Transversal Parallel Lines Alternate Interior Angles
Vocabulary Builder
Congruent Statement Angle Measure Congruent Polygons
Congruent Segments Congruent Triangles Proof
Algebraic EquationSegment Measure
Congruent Angles
Vocabulary Builder
Addition PropertyDivision Property
Reflexive Property
Transitive Property Symmetric Property Multiplication Property
Distributive Property Subtraction Property Substitution Property
Vocabulary Builder
Vertical Angles TheoremCongruent Complements
Theorem Congruent Supplements Theorem
All right angles are congruent
If two angles are congruent and supplementary, then each is a
right angle
Unit 2: Congruence, Similarity, & Proofs
2.8 Parallel Lines and Transversals
2.8 Parallel Lines and Transversals
Transversal
Lie between the two lines
On same side of the transversal
Lie outside the two lines
On opposite sides of the transversal
On opposite sides of the transversal
1, 2, 5, 6
1 and 6, 2 and 5
1 and 5, 2 and 6
1 and 6, 2 and 5
3, 4, 7, 8
2.8 Parallel Lines and Transversals
VerticalConsecutive
InteriorAlternate Interior
Alternate Exterior
VerticalConsecutive
Interior
Alternate Exterior Alternate Exterior
VerticalConsecutive Interior
Vertical Alternate Interior
45Vertical angles are congruent
45Alternate Interior angles are congruent
135Consecutive interior angles are supplementary
135Linear pairs are supplementary
2.8 Parallel Lines and Transversals
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Consecutive
Supplementary
𝑚∠1 = ______
𝑚∠2 = ________
𝑚∠3 = _______
𝑚∠4 = ________
𝑚∠5 = ________
𝑚∠6 = ________
𝑚∠7 = ________
40
140
140
40
140
140
40
𝑚∠1 = ______
𝑚∠2 = ________
𝑚∠3 = _______
𝑚∠4 = ________
𝑚∠5 = ________
𝑚∠6 = ________
𝑚∠7 = ______
𝑚∠8 = ________
𝑚∠9 = _______
𝑚∠10 = ________
𝑚∠11 = ________
𝑚∠12 = ________
35
80
80
100
65
65
65
115
65
115
100
80
𝑚∠1 = ______
𝑚∠2 = ________
𝑚∠3 = _______
𝑚∠4 = ________
𝑚∠5 = ________
𝑚∠6 = ________
𝑚∠7 = ________
𝑚∠8 = ______
𝑚∠9 = ________
𝑚∠10 = _______
𝑚∠11 = ________
𝑚∠12 = ________
𝑚∠13 = ________
𝑚∠14 = ________
102
78
102
78
102
78
102
102
78
102
78
102
102
78
