6.2 – use proportions to solve geometry problems
DESCRIPTION
6.2 – Use Proportions to Solve Geometry Problems. Complete the statement. y. If. , then. x. Complete the statement. x. If. , then. y. Complete the statement. 9+ y. If. , then. y. Complete the statement. 5+11. If. , then. 11. - PowerPoint PPT PresentationTRANSCRIPT
6.2 – Use Proportions to Solve Geometry Problems
Property Result
Reciprocal Property
Interchange Means
Adding
,a c
If thenb d
=
,a c
If thenb d
=
a b c d
b d
+ +=
b d
a c=
a b
c d=
,a c
If thenb d
=
Complete the statement.
y
x=
107
?
?
7
10=If , then
y
x
?
?
24
6=If , then
x
y
Complete the statement.
yx
246=
?
?3=
+xxIf , then 9+y
y
Complete the statement.
yx
93=
?
?=
+yyx
If , then 5+1111
Complete the statement.
11
5=
yx
Use the given information and the diagram to find the unknown length.
1
x=
3x = 2
x =23
3
2
Use the given information and the diagram to find the unknown length.
3
4=
3x = 24
x = 8
6
x
Use the given information and the diagram to find the unknown length.
12
x=
18x = 180
x = 10
18
15
Use the given information and the diagram to find the unknown length.
12
9=
12x = 144
x = 12
16
x
6.3 – Use Similar Polygons
Similar Polygons:
• Corresponding angles are congruent
• Corresponding sides are proportional
Scale Factor:
The ratio of the lengths of two corresponding sides of similar figures.
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.
=DE
AB
Angles
A D
B E
C F
Sides: =EF
BCDF
AC
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.
=MJ
CD
Angles
C M
D J
E K
Sides: =JK
DE
ML
CF
F L
=KL
EF
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor.
Angles
A F
B D
C E
Sides: =6
3
2
1
=10
5
2
1
=8
4
2
1
Yes, they are similar.
ABC ~
Scale factor:2
1
FDE
Angles
Q W
R X
S YT Z
Sides: =3
6
1
2
=6
8
3
4
No, they are not similar.
The polygons are similar as noted. Find the value of x.
6
4=
6x = 48
x = 8
12
x
The polygons are similar as noted. Find the value of x.
8
12=
8x = 144
x = 18
BCED ~ KLMJ12
x
The two triangles are similar. Find the values of the variables.
6
12=
6m = 66
m = 11
6
12=
12n = 48
n = 4
5.5
m 8
n
5. The two figures are similar. Find the scale factor of their sides. Then find the ratios of their perimeters. What do you notice?
18
6 4
12128
Scale Factor:12
8=
3
2
Ratio of Perimeters:36
24=
3
2
They are the same!
Ratios of Perimeters:
If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths
ratioperimeters
side
The ratio of one side of a picture to the corresponding side of a larger picture is 2:7. The perimeter of the smaller picture is 16 inches. Find the perimeter of the larger picture.
2
7=
2x = 112
x = 56in
2
7
16x
16
x
In the diagram, MNOP ~ WXYZ .
a.Find the scale factor of MNOP to WXYZ .
5
4
10
8=
In the diagram, MNOP ~ WXYZ .
b. Find the values of x, y, and z.
5
4=
4x = 60
x = 15
5
4=
5y = 40
y = 8
z° = 135°12
x 10
y
In the diagram, MNOP ~ WXYZ .
c. Find the perimeter of MNOP.
10 + 15 + 10 + 15
50
d. Find the ratio of the perimeter of MNOP to the perimeter of WXYZ.
In the diagram, MNOP ~ WXYZ .
12 + 8 + 12 + 8
40
PerimeterMNOP
PerimeterWXYZ=
5
4
50
40=
HW Problem
6.3 # 12
Ans:
6.2
6.3
367-369
376-378
3-11 odd, 12, 16-18, 28, 29
3, 7-12, 19, 20, 31, 32
36in5
3=
60x