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104_G6U13_TG 2014.4.17 6:55 PM ˘ ` 188
Activity 3 Unknown Measures
jOb ective Determine unknown angles and sides based on known similar figures.
1. Textbook Instructions Activity 3 Unknown Measures
In this activity students learn to use similar 1 . The pair of shapes are similar figures. Find the unknown angle.
figures and the principles of corresponding
angles and sides to find the values of Find the value of angle b. E H
unknown angles and sides. 120Ø 60Ø
AD
1. Building on the previous activity, this 120Ø b
problem set asks students to determine an
unknown angle by finding the corresponding 60Ø 120Ø 60Ø 120Ø
angle of a similar figure for which all angles BC F G
are provided. Thus, in the sample problem
unknown angle B corresponds to angle H, All corresponding angles (angles that match) are congruent.
which has a known angle of 60 degrees; thus
angle B is also 60 degrees. Find the corresponding angle of b.
b= H
Have students solve the problems.
1a. The unknown angle D corresponds to Corresponding angles are congruent.
known angle A and is thus 60 degrees. H = 60
1b. Note that right angles D and H are not
marked with values in degrees, but with a So, b = 60
symbol that identifies both as right (90
degree) angles. This allows identification of a. D
angle E as corresponding to known angle A. d
A
Find the corresponding
60Ø angle of d.
d= A
70Ø 50Ø So, d = 60Ø
B C 70Ø
E 50Ø
F
b. H
D E Find the corresponding
A f
angle of f.
120Ø f= A
So, f = 120Ø
70Ø 80Ø 80Ø
B C 70Ø G
F
114
2. Build Understanding
Solving these problems requires determining that the reference shapes are not only “similar” in the everyday
sense but formally similar, having identical angles (and proportional sides).
The underlying principle of congruency is that if an unknown figure has all but one angle specified and is
similar to a known figure for which all angles are provided, the single unknown angle will be equal to the
corresponding angle in the known figure.
What if two angles are unknown? In that case we cannot be certain that the figures are, in fact, formally
similar, even if they have a generally “similar” appearance.
188 NUMINO Teacher s Guide
Activity 3 Unknown Measures
jOb ective Determine unknown angles and sides based on known similar figures.
1. Textbook Instructions Activity 3 Unknown Measures
In this activity students learn to use similar 1 . The pair of shapes are similar figures. Find the unknown angle.
figures and the principles of corresponding
angles and sides to find the values of Find the value of angle b. E H
unknown angles and sides. 120Ø 60Ø
AD
1. Building on the previous activity, this 120Ø b
problem set asks students to determine an
unknown angle by finding the corresponding 60Ø 120Ø 60Ø 120Ø
angle of a similar figure for which all angles BC F G
are provided. Thus, in the sample problem
unknown angle B corresponds to angle H, All corresponding angles (angles that match) are congruent.
which has a known angle of 60 degrees; thus
angle B is also 60 degrees. Find the corresponding angle of b.
b= H
Have students solve the problems.
1a. The unknown angle D corresponds to Corresponding angles are congruent.
known angle A and is thus 60 degrees. H = 60
1b. Note that right angles D and H are not
marked with values in degrees, but with a So, b = 60
symbol that identifies both as right (90
degree) angles. This allows identification of a. D
angle E as corresponding to known angle A. d
A
Find the corresponding
60Ø angle of d.
d= A
70Ø 50Ø So, d = 60Ø
B C 70Ø
E 50Ø
F
b. H
D E Find the corresponding
A f
angle of f.
120Ø f= A
So, f = 120Ø
70Ø 80Ø 80Ø
B C 70Ø G
F
114
2. Build Understanding
Solving these problems requires determining that the reference shapes are not only “similar” in the everyday
sense but formally similar, having identical angles (and proportional sides).
The underlying principle of congruency is that if an unknown figure has all but one angle specified and is
similar to a known figure for which all angles are provided, the single unknown angle will be equal to the
corresponding angle in the known figure.
What if two angles are unknown? In that case we cannot be certain that the figures are, in fact, formally
similar, even if they have a generally “similar” appearance.
188 NUMINO Teacher s Guide
