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P. 206
104_G6U13_TG 2014.4.17 6:55 PM ˘ ` 189
13Scale Down, Scale Up Unit
2 . The pair of shapes are similar figures. Find the length of the unknown 2. These problems closely resemble the last
set, except that they deal with corresponding
side. sides of similar figures rather than
corresponding angles.
Find the measure of a. Find pairs of corresponding sides.
A 3 cm D EF and AB Solving these problems thus requires an
a and AD additional step, because while the angles of
4 cm similar figures are identical, the sides of
similar figures are only proportional.
BC H Corresponding sides are proportional. Thus, after determining corresponding
Ea EF = a sides, the length of the unknown side
AB AD cannot simply be read from the known
8 cm similar reference figure, but must be
calculated based on proportionality.
So, 8 = a Example: Find the measure of a.
4 3 The unknown side EH has the same
FG proportion to known side EF (8 cm) as the
All corresponding sides Cross multiply. corresponding side AD in the reference
(sides that match) 8 3=4 a figure (3 cm) has to side AB (4 cm). Cross
are proportional. a = 6 (cm) multiplication shows that side EH is
therefore 6 cm.
a. E a cm H EF = EH
AB AD Have students find the length of the missing
G sides.
A 6 cm D H so, 15 = a
5 cm 15 cm 5 6
12 cm
B CF G 15 6 = 5 a
a = 18 (cm)
b. E EF = GH
8 cm AB CD
A
6 cm D so, 8 = 12
e cm 6 e
B
8 e = 6 12
e = 9 (cm)
CF
13. Scale Down, Scale Up 115
As with the previous problem set, solving these problems depends on understanding the principle of
congruence, but further calls for successfully setting up a cross-multiplication.
It is important for students to keep the relevant proportions clearly in mind. The sample problem can be
expressed in words as “The unknown side EH has the same proportion to 3 cm as 4 cm relates to 8
cm. Since 4 is half of 8, we can thus say that side EH is double 3, or 6 cm.
6A Unit 13 189
13Scale Down, Scale Up Unit
2 . The pair of shapes are similar figures. Find the length of the unknown 2. These problems closely resemble the last
set, except that they deal with corresponding
side. sides of similar figures rather than
corresponding angles.
Find the measure of a. Find pairs of corresponding sides.
A 3 cm D EF and AB Solving these problems thus requires an
a and AD additional step, because while the angles of
4 cm similar figures are identical, the sides of
similar figures are only proportional.
BC H Corresponding sides are proportional. Thus, after determining corresponding
Ea EF = a sides, the length of the unknown side
AB AD cannot simply be read from the known
8 cm similar reference figure, but must be
calculated based on proportionality.
So, 8 = a Example: Find the measure of a.
4 3 The unknown side EH has the same
FG proportion to known side EF (8 cm) as the
All corresponding sides Cross multiply. corresponding side AD in the reference
(sides that match) 8 3=4 a figure (3 cm) has to side AB (4 cm). Cross
are proportional. a = 6 (cm) multiplication shows that side EH is
therefore 6 cm.
a. E a cm H EF = EH
AB AD Have students find the length of the missing
G sides.
A 6 cm D H so, 15 = a
5 cm 15 cm 5 6
12 cm
B CF G 15 6 = 5 a
a = 18 (cm)
b. E EF = GH
8 cm AB CD
A
6 cm D so, 8 = 12
e cm 6 e
B
8 e = 6 12
e = 9 (cm)
CF
13. Scale Down, Scale Up 115
As with the previous problem set, solving these problems depends on understanding the principle of
congruence, but further calls for successfully setting up a cross-multiplication.
It is important for students to keep the relevant proportions clearly in mind. The sample problem can be
expressed in words as “The unknown side EH has the same proportion to 3 cm as 4 cm relates to 8
cm. Since 4 is half of 8, we can thus say that side EH is double 3, or 6 cm.
6A Unit 13 189
