Embed Size (px)
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 Presentation
Citation preview
6.2 – Use Proportions to Solve Geometry Problems
Property Result
Reciprocal Property
Interchange Means
Adding
,a cIf thenb d
,a cIf thenb d
a b c db d
b da c
a bc d
,a cIf thenb d
Complete the statement.
yx
107
??
710
If , then yx
??
246
If , then xy
Complete the statement.
yx246
??3
xxIf , then 9+y
y
Complete the statement.
yx93
??
yyxIf , then 5+11
11
Complete the statement.
115
yx
Use the given information and the diagram to find the unknown length.
1x
3x = 2
x = 23
32
Use the given information and the diagram to find the unknown length.
34
3x = 24
x = 8
6x
Use the given information and the diagram to find the unknown length.
12x
18x = 180
x = 10
1815
Use the given information and the diagram to find the unknown length.
129
12x = 144
x = 12
16x
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.
DEAB
AnglesA DB EC F
Sides: EFBC
DFAC
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.
MJCD
AnglesC MD JE K
Sides: JKDE
MLCF
F L
KLEF
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor.
AnglesA FB DC E
Sides: 63
21
105
21
84
21
Yes, they are similar.
ABC ~
Scale factor:21
FDE
AnglesQ WR XS YT Z
Sides: 36
12
68
34
No, they are not similar.
The polygons are similar as noted. Find the value of x.
64
6x = 48
x = 8
12x
The polygons are similar as noted. Find the value of x.
812
8x = 144
x = 18
BCED ~ KLMJ12x
The two triangles are similar. Find the values of the variables.
5.5m
6m = 66m = 11
612 8
n
The two triangles are similar. Find the values of the variables.
5.5m
6m = 66m = 11
12n = 48n = 4
612 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: 128
32
Ratio of Perimeters:3624
32
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.
27
2x = 112x = 56in
2
7
16x
16x
7. In the diagram, WXYZ ~ BCDE.
a.Find the scale factor of WXYZ to BCDE.
64
32
7. In the diagram, WXYZ ~ BCDE.
b. Find the values of XY and YZ.32
3XY
6YZ
2XY = 9
XY = 4.5
4.5 4.5
7. In the diagram, WXYZ ~ BCDE.
b. Find the values of XY and YZ.32
3XY
6YZ
2YZ = 18
YZ = 9
2XY = 9
XY = 4.5
4.5 4.5
9
7. In the diagram, WXYZ ~ BCDE.
c. Find mC.
mC = 117°4.5 4.5
9
d. Find the perimeter of WXYZ.
7. In the diagram, WXYZ ~ BCDE.
4.5 4.5
99 + 4.5 + 4.5 + 6
24u
HW Problem
6.3 # 12
6.26.3
367-369376-378
3-11 odd, 12, 16-18, 28, 293, 7-12, 19, 20, 31, 32
x = 36in
53
60x
35
x60
