Download Geometry Chapter 6 Review

Name: ______________________
Class: _________________
Date: _________
Geometry Chapter 6 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Determine whether each pair of figures is similar. Justify your answer.
____
1.
a.
b.
c.
d.
ΔDEF ∼ ΔCBA because the corresponding angles are congruent.
ΔDEF is not similar to ΔCBA because the corresponding angles are not congruent.
ΔDEF ∼ ΔCBA because the ratio of the corresponding sides is proportional and the
corresponding angles are congruent.
ΔDEF is not similar to ΔCBA because the ratio of the corresponding sides is not
proportional.
1
ID: A
Name: ______________________
____
ID: A
2. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
Identify and describe the transformation.
D: (x, y) → (4x, 4y)
A(2, 1), B(4, 1), C(4, − 3)
a.
b.
c.
d.
This is a dilation
–12).
This is a dilation
This is a dilation
C’(1, –0.75).
This is a dilation
–0.75).
about (0, 0) with a scale factor of 0.25; A’(8, 4), B’(16, 4), C’(16,
about (0, 0) with a scale factor of 4; A’(8, 4), B’(16, 4), C’(16, –12).
about (0, 0) with a scale factor of 0.25; A’(0.5, 0.25), B’(1, 0.25),
about (0, 0) with a scale factor of 4; A’(0.5, 0.25), B’(1, 0.25), C’(1,
Short Answer
Solve each proportion.
3.
x+1
14
=
x−1
20
2
Name: ______________________
ID: A
Identify the similar triangles. Find x.
4.
Determine whether each pair of triangles is similar. Justify your answer.
5.
Find x and the measures of the indicated parts.
6. AB
7. EB and ED
3
Name: ______________________
ID: A
8. BC and AC
9.
BD and CE
BD = 4x
CE = 2x + 2
10. Find x so that QS Ä PT.
PQ = 8, QR = 5, RS = 15, ST = x + 3
4
Name: ______________________
ID: A
11. Determine whether QS Ä PT. Justify your answer.
PQ = 18, QR = 6, RS = 12, ST = 36
Find the perimeter of the given triangle.
12.
ABC, if
ABC ∼
PQR, perimeter of
PQR = 36, AC = 12, PR = 6
13.
PQR, if
PQR ∼
PST, QR = 15, ST = 10, PS = 9, and PT = 8
5
Name: ______________________
ID: A
14. Find PS if ABC ∼ PQR, AD is an altitude of
PQR, AD = 12, AC = 16, and PR = 10.
ABC, PS is an altitude of
15. Find AB if BD and QS are altitudes and
PQR.
ABC ∼
16. Are the two triangles similar? How do you know?
Which theorem or postulate proves the two triangles are similar?
17.
6
Name: ______________________
ID: A
18.
19. Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points.
D: (x, y) → (3x, 3y)
J(1, 4), K(6, 4), L(6, 1), M(1, 1)
7
ID: A
Geometry Chapter 6 Review
Answer Section
MULTIPLE CHOICE
1. ANS: B
2. ANS: B
MSC: DOK 2
SHORT ANSWER
3. ANS:
17
−3
4. ANS:
ΔABC ∼ ΔEDF; x = 3
5. ANS:
yes; ΔEDF ∼ ΔBCA by SAS Similarity
6. ANS:
x = 7, AB = 20
7. ANS:
x = 3, EB = 15, ED = 42
8. ANS:
x = 6, BC = 10, AC = 12
9. ANS:
x = 5, BD = 20, CE = 12
10. ANS:
21
11. ANS:
PQ ST
yes,
=
=3
QR SR
12. ANS:
72
13. ANS:
40.5
14. ANS:
7.5
15. ANS:
6
16. ANS:
yes, by AA∼
MSC: DOK 2
17. ANS:
AA Postulate
MSC: DOK 2
1
ID: A
18. ANS:
AA∼ Postulate
MSC: DOK 2
19. ANS:
J´(3, 12), K´(18, 12),
L´(18, 3), M´(3, 3)
MSC: DOK 2
2