Download Project Problems Set 2 Module 4 1. The polygon Q(3, 2), R(6, 5), S(6

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Transcript
Name _______________________________________ Date ___________________ Class __________________
Project Problems Set 2
Module 4
1. The polygon Q(3, 2), R(6, 5), S(6, 2)
undergoes the transformation:
(x, y)  (4x, 4y). Name the coordinates
of the image points.
8. In the figure, PQR  UVW. What is
mR?
2. The angles of a triangle measure 4,
86, and 90. Which classification of
the triangle is correct?
3. Which could be the angle measures
of an acute triangle?
A 32-56-92
C 34-56-90
B 33-58-91
D 35-56-89
4. What is the length of the longest side
of the triangle?
5. What is mW ?
6. Two angles of a triangle measure 22 and
53. What is the measure of the
third angle?
7. What is the value of x if the acute angles
of a right triangle measure 8x and 12x?
9. If KMQ  WJR, which segment is
congruent to RW ?
10. Which angle is congruent to Z if
ZLV  SPN ?
11. If ABC  KJC, which statement is NOT
necessarily true?
12. Suppose S  N, J  I,
A  T, JS  IN, JA  IT , and
AS  TN. Write a congruency statement
for the two triangles.
13. The transformation M:
(x, y)  (0.5x, 0.5y) has been applied
to the polygon KLM. If the point M had
coordinates (4, 4), name the
coordinates of the image of M.
________________________________________
14. Is the polygon K(5, 4), L(5, 6), M(7, 6)
congruent to the polygon N(4, 3), P(4,
5), Q(6, 5)?
________________________________________
Use the figure for Exercises 15 and
16.
15. Classify the triangle by its angle
measures.
________________________________________
21. Complete the statement. Two triangles
are congruent if and only if their
_______ angles and sides are
congruent.
________________________________________
Use the figure for Exercises 22 and
23.
22. What value of x proves ABC  DEF
by SAS?
________________________________________
________________________________________
16. Classify the triangle by its side lengths.
________________________________________
17. Complete the sentence. All of the angles
in an equilateral triangle measure
_________.
23. If AB  DE , what additional
congruence statement is needed to
prove ABC  DEF by SSS?
________________________________________
Use the figure for Exercises 24 and
25.
________________________________________
18. What is the measure of 1?
24. Write True or False. You can use AAS
to prove ABE  CDE.
________________________________________
________________________________________
19. Given: GHJ  NOP. What is the
value of x?
________________________________________
20. If KLM  RST, what is the value
of x?
25. What additional congruence statement
is needed to prove ABE  CDE by
HL?
Module 5
1. If x= 5 is RST  UVW ? Explain.
6. When using HL congruence theorem, what
type of triangles do you need?
7. Find the value of x.
.
2. What additional information is needed to
prove MNP  PQM by SAS?
8.What is the measure of one of the base
angles of an isosceles triangle if the
measure of the vertex angle is 98?
9. One angle of an equilateral triangle
measures (4x  20). What is the value of
x?
3. A parachute jumper called into the airport
to be rescued by helicopter. She said her
pilot flew 8 kilometers west and then
headed due north about 20 minutes
before she jumped. Does the helicopter
pilot have enough information to locate
her exact location? Explain.
10. Suppose MWR  CYQ, MW  8,
WR  9, and CQ  10. What is MR?
F 8
H 10
G 9
J 11
11. Write True or False and explain.
4. Which congruence theorem CANNOT be
used to prove
MNK  KLM?
5.In the figure, H is the midpoint of EK and
FJ . What reason can be used in a proof
to show EF  JK ?
Given: ABC and DEF. To use CPCTC to
prove A  D, you must first prove
ABC  DEF.
12. What postulate or theorem proves
K  M?
Module 8
1. Which is similar to this quadrilateral?
A
C
B
D
6. The scale on a map uses 3 centimeters
to represent 4 kilometers. The distance
between two towns on the map is 6
centimeters. How many kilometers
apart are the towns?
7. The coordinates of PMN are P(2, 10),
M(8, 6), and N(4, 2). After a dilation,
the image of P is (19, 95). What are the
coordinates of the image of M?
2. Complete the similarity statement.
8. Determine whether the triangles are similar.
If so, write the similarity ratio
and a similarity statement.
ABC 
?
3. The dilation D: (x, y)  (0.2x, 0.2y) has
been applied to the polygon S(–5, 5),
T(–5, 10), U(5, 15). What are the
coordinates of the image points?
4. Which transformation(s) can be used to
show that polygon W(–2, 4), X(–2, 8),
Y(–6, 2), Z(–10, 4) is similar to polygon
L(–3, 0), M(–3, 2), N(–5, –1), O(–7, 0)?
5. To measure the distance across a pond,
a surveyor locates points A, B, C, D, and
E as shown. What is AB to the nearest
meter?
9. Give the definition of a dilation.
10. Name the dilation and then the translation
that was used to map O(2, 5), P(6,1),
Q(0, –1), R(–1, 0) to A(8, 14), B(16, 6),
C(4, 2), D(2, 4).
11. Given that UOV is a dilation image of
SOT, find the coordinates of V and the
scale factor.
11