Review for Mastery
Name ________________________________________ Date___________________ Class _________________ LESSON
5-5
Review for Mastery Similar Figures Similar Polygons
Congruent Polygons
same shape corresponding angles are congruent !A " !A', !B " !B', !C " !C'
same shape corresponding angles are congruent !A " !A', !B " !B', !C " !C'
usually different size corresponding sides are in proportion AB BC AC = = A'B' B'C' A'C'
same size corresponding sides are congruent AB ! A'B', BC ! B'C', AC ! A'C '
Complete to tell if the polygons are similar. 1. a. corresponding angles: !A and ________, !B and ________, !C and ________, !D and ________
b. all corresponding angles congruent? ________ c. corresponding sides: AB and ________,
BC and ________, CD and ________,
AD and ________ d. The ratio of each pair of corresponding sides is:
AB
= ________,
BC
= ________,
CD
= ________,
AD
= ________
e. Are the corresponding sides proportional? Explain. _____________________________________________________________________________________
f. The scale factor is the simplest form of the ratio of the corresponding sides. What is the scale factor for these parallelograms?
_________________
g. Are the parallelograms similar? Explain. _____________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
45
Holt McDougal Mathematics
Name ________________________________________ Date___________________ Class _________________ LESSON
5-5
Review for Mastery Similar Figures (continued)
Use the scale factor to find a missing dimension. 6 2 scale factor = or 9 3 Since EF corresponds to BC , multiply EF by the scale factor to find BC. 2 BC = (15) = 10 m 3 Complete to find each missing dimension. 2.
3.
scale factor
PQ = _______ or _______ JK
scale factor =
MA = _______ or _______ RO
RQ = scale factor • (KL)
MH = scale factor • (RE)
RQ = _______ × _______ or _______cm
MH = _______ × _______ or _______in.
Use a proportion to find a missing dimension. Corresponding sides are in proportion.
AB BC = DE EF 6 BC = 9 15 9(BC) = 90 BC = 10 m Complete to find the missing dimension. MH 4. = _____ RE MH = _____ 6 _____ ! (MH ) = _____ MH = _____ in.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
46
Holt McDougal Mathematics
7. C 9. B
8. F 10. J
6. 30 cm long by 22 cm wide 7. 8 cm × 6.05 cm 8. 199.5 ft
Reading Strategies
1. 2. 3. 5. 7. 9.
The cross products will be equal. The cross products are not equal. no 4. yes no 6. yes no 8. yes no 10. yes
Review for Mastery
1. a. !E ; !F ; !G ; !H b. yes c. EF ; FG ; GH ; EH d. EF,
Puzzles, Twisters & Teasers
1. H 3. G 5. S 7. H 9. O H I G H
2. 4. 6. 8. 10. S C H O O
e. yes; equal cross products
I H C O L L
8 10
2.
60 = 60
4 2 ; 10 5 2 ; 12; 4.8 5
1. ABC ~ RST ~ JMK 2. NOPQ and BCDE 3.
4. 24 in.
14 7 ; 8 4 7 ; 6; 10.5 4
6. 6 in. × 7.5 in.
7. 2 ft 4.
Practice B
1. QRS ~ XZY 3. 90 cm 5. 18 cm × 27 cm
? =
4 5 g. yes; corresponding !s congruent, corresponding sides proportional
Practice A
2 1 5. 36 in.
6 ; 7.5
f.
LESSON 5-5
3.
6 8 6 8 ; FG, ; GH, ; EH; 7.5 10 7.5 10
2. 13.5 in. 4. 84 in. 6. 12.5 in.
MA 14 ; RO 8 8; 84; 10.5
Challenge
4 2 AB = or 6 3 DE 2. a. 12 cm b. 18 cm
7. 7
1.
Practice C
1. x = 18
2. x = 63
3. x = 30
4. x = 40
2 3 3. The ratio of the perimeters of two similar triangles is the same as the ratio of similitude.
5. AB = 18 cm,
c.
BC = 10 cm, AC = 14 cm
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
81
Holt McDougal Mathematics
5-5
Review for Mastery Similar Figures Similar Polygons
Congruent Polygons
same shape corresponding angles are congruent !A " !A', !B " !B', !C " !C'
same shape corresponding angles are congruent !A " !A', !B " !B', !C " !C'
usually different size corresponding sides are in proportion AB BC AC = = A'B' B'C' A'C'
same size corresponding sides are congruent AB ! A'B', BC ! B'C', AC ! A'C '
Complete to tell if the polygons are similar. 1. a. corresponding angles: !A and ________, !B and ________, !C and ________, !D and ________
b. all corresponding angles congruent? ________ c. corresponding sides: AB and ________,
BC and ________, CD and ________,
AD and ________ d. The ratio of each pair of corresponding sides is:
AB
= ________,
BC
= ________,
CD
= ________,
AD
= ________
e. Are the corresponding sides proportional? Explain. _____________________________________________________________________________________
f. The scale factor is the simplest form of the ratio of the corresponding sides. What is the scale factor for these parallelograms?
_________________
g. Are the parallelograms similar? Explain. _____________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
45
Holt McDougal Mathematics
Name ________________________________________ Date___________________ Class _________________ LESSON
5-5
Review for Mastery Similar Figures (continued)
Use the scale factor to find a missing dimension. 6 2 scale factor = or 9 3 Since EF corresponds to BC , multiply EF by the scale factor to find BC. 2 BC = (15) = 10 m 3 Complete to find each missing dimension. 2.
3.
scale factor
PQ = _______ or _______ JK
scale factor =
MA = _______ or _______ RO
RQ = scale factor • (KL)
MH = scale factor • (RE)
RQ = _______ × _______ or _______cm
MH = _______ × _______ or _______in.
Use a proportion to find a missing dimension. Corresponding sides are in proportion.
AB BC = DE EF 6 BC = 9 15 9(BC) = 90 BC = 10 m Complete to find the missing dimension. MH 4. = _____ RE MH = _____ 6 _____ ! (MH ) = _____ MH = _____ in.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
46
Holt McDougal Mathematics
7. C 9. B
8. F 10. J
6. 30 cm long by 22 cm wide 7. 8 cm × 6.05 cm 8. 199.5 ft
Reading Strategies
1. 2. 3. 5. 7. 9.
The cross products will be equal. The cross products are not equal. no 4. yes no 6. yes no 8. yes no 10. yes
Review for Mastery
1. a. !E ; !F ; !G ; !H b. yes c. EF ; FG ; GH ; EH d. EF,
Puzzles, Twisters & Teasers
1. H 3. G 5. S 7. H 9. O H I G H
2. 4. 6. 8. 10. S C H O O
e. yes; equal cross products
I H C O L L
8 10
2.
60 = 60
4 2 ; 10 5 2 ; 12; 4.8 5
1. ABC ~ RST ~ JMK 2. NOPQ and BCDE 3.
4. 24 in.
14 7 ; 8 4 7 ; 6; 10.5 4
6. 6 in. × 7.5 in.
7. 2 ft 4.
Practice B
1. QRS ~ XZY 3. 90 cm 5. 18 cm × 27 cm
? =
4 5 g. yes; corresponding !s congruent, corresponding sides proportional
Practice A
2 1 5. 36 in.
6 ; 7.5
f.
LESSON 5-5
3.
6 8 6 8 ; FG, ; GH, ; EH; 7.5 10 7.5 10
2. 13.5 in. 4. 84 in. 6. 12.5 in.
MA 14 ; RO 8 8; 84; 10.5
Challenge
4 2 AB = or 6 3 DE 2. a. 12 cm b. 18 cm
7. 7
1.
Practice C
1. x = 18
2. x = 63
3. x = 30
4. x = 40
2 3 3. The ratio of the perimeters of two similar triangles is the same as the ratio of similitude.
5. AB = 18 cm,
c.
BC = 10 cm, AC = 14 cm
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
81
Holt McDougal Mathematics
