2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
Tuesday, 1/3/2017
Do Now:
- Take out Notebooks
- Copy HW
Finish Classwork
Proportions:
A proportion tells us that two ratios, (or fractions) are equal.
These ratios are the same, so 1/3 is proportional to 2/6!
Give a ratio that is proportional to 2/3:
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
You can tell if 2 ratios are proportional by using cross
multiplication. This requires us to multiply diagonally across the
equal sign to see if we find equivalent products.
Are these ratios proportional?
1
6
?
=
18
4
2 = 8 ?
20
5
3 = 16 ?
48
9
3 =1 ?
5 3
Find the missing value by solving the equation given by cross
multiplying:
1
7
=
x
63
2
8
=
5
x
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
Similar Triangles have
Proportional Side Lengths
What does SIMILAR mean?
Similar Figures have the same shape but may have different sizes.
B
Angles are congruent. Corresponding Sides are in proportion.
B'
A
C
A'
C'
~ A'
A=
~
B = B'
~ C'
C=
Always list the corresponding parts of the similar triangles in the same order.
CA
AB = BC
=
A'B' B'C' C'A'
AB corresponds to A'B'
BC corresponds to B'C'
CA corresponds to C'A'
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
Proving Triangles Similar
Using Triangle Sides
Prove that Corresponding Side Lengths are in Proportion
Ex
A D
3
F
5
4
9
15
E
C
B
12
Prove that ABC ~ DEF
What is the Constant of Proportionality?
Determine if RST and UVW are similar.
U
R
3
S 5
4
12
T
V
20
16
What is the Constant of Proportionality?
W
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
Finding missing measures in similar triangles:
ABC ~ ADE
B
x ft
Find x
D
0.8 ft
C
E
7 ft
14 ft
Solve for the missing side length
A
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017
2017­1­3 Proportions Review and Similar Triangles.notebook
January 03, 2017