Download Semester 1 Closure

Semester 1 Closure
Geometer:
CPM Chapters 1-6
Period:
DEAL
 Take time to review the notes we have taken in class so far and previous closure packets. Look for
concepts you feel very comfortable with and topics you need more help with. Look for connections
between ideas as well as connections with material you learned previously.
Chapter 1: Shapes and Transformations
Chapter 2: Angles and Measurements
Chapter 3: Justification and Similarity
Chapter 4: Trigonometry and Probability
Chapter 5: Completing the Triangle Toolkit
Chapter 6: Congruent Triangles
For questions 1-6, use the figure to the right.
1) What is different name for plane R. ____________________
2) What is different name for  1. ________________________
3) What is different name for line m. ______________________
4) Name a pair of congruent segments. ____________________
5) Name three collinear points. __________________________
6) Name a pair of supplementary angles. __________________
7) Name the transformation(s) that are not isometric. Justify your answer.
8) Using transformations show that a||b.
9) Use the following regular hexagon to answer the following questions.
A) Name the image of B after a 240 clockwise rotation about Z.
B) Name the image of A reflected over 𝐹𝐶.
10) Find the measure of the numbered angles.
m∠1 = ___________
m∠1 = ___________
m∠1 = ___________
11) Given a || b cut by a transversal c, which of the following statements is not true.
A)
B)
C)
D)
 1 and  3 are corresponding angles
 2 and  3 are same-side int. angles
 3 and  4 are vertical angles
 1 and  4 are alternate int. angles
12) Refer to the diagram to answer the following questions:
Assume the lines are parallel.
A) Name a pair of same-side interior angles.
B) Name a pair of corresponding angles.
C) Name a pair of alternate interior angles.
13) Write the coordinates of the vertices of the image ABCD for each transformation.
A) Translation (x, y)  (x + 4, y – 2)
B) reflection across x = -1
C) rotation of 180o about the origin
D) Dilation with scale factor of 2 about the origin
m∠1 = ___________
m∠2 = ___________
m∠3 = ___________
m∠4 = ___________
14) Complete the transformations below and then answer the corresponding questions.
a. Reflect JKLM across the y-axis to form J’K’L’M’.
Then rotate J’K’L’M’ 90o counterclockwiseabout the origin to form J’’K’’L’’M’’.
b. What single rigid transformation transforms JKLM to J’’K’’L’’M’’?
15) How many lines of symmetry does a square have? Hint: Draw a diagram.
16) Classify the triangle by its sides.
a. ______________________
b. ______________________
17) Classify the triangle by its angles.
18) Find the value of x.
19) Find the value of x if AC = 20.
20) Find the value of x if B is the midpoint of 𝑨𝑪.
21) Find mTQM .
22) Find the value of x.
23) Find the value of x.
24) Find the measure of the sides of equilateral ∆JKL if JK = 5x – 7 and JL = 2x + 5.
25) ⃗⃗⃗⃗⃗⃗
𝑸𝑿 bisects  PQR. If m 1 = 4x -12 and m 2 = 2x + 6, find m XQR.
26) Find the value of x.
27) Find the value of x and y. State geometric relationships used in solving.
28) Find the value of x and y.
Multiply each expression below.
29) (2𝑑 − 3)(𝑑 + 4)
32) Find the intersection of MN and LO .
30) 2𝑥(𝑥 + 3)
31) (𝑟 − 5)2
33) Find the slope of a line perpendicular to 3y + 2x = 4.
34) What is the slope of the line that contains (6, -4) and (-4, 1)?
35) Which pair of lines is perpendicular?
a. y = 3x + 5
b. y = 4x – 5
c. y = 5x – 3
y = -3x – 8
y = 4x + 2
y = 5x + 3
b. y = -2x – 1
2x + y = 4
c. y = 3x + 8
3x + y = 6
1
3
y = 2x – 5
36) Which pair of lines is parallel?
a. 𝑦 = 5𝑥 + 3
5x + y = 10
37) a. Graph a line parallel to y = 3x – 1 that contains (2, 3).
b.Write the equation of the new line in point slope form.
1
38) a. Graph a line perpendicular to y = 2x – 5 that contains (-2, 2).
b. Write the equation of the new line in slope-intercept form.
2
3
d. y = − 𝑥 − 11
d. x = 3
y=3
39) What is the distance between (-1, 6) and (5, -2)?
40) The two rectangles are similar. Which is a correct proportion for corresponding sides?
4m
8m
12 m
x
a.
b.
c.
d.
41) The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the
height of the model to the height of the actual Sears Tower?
42) Solve the proportion.
43) The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second.
The figures are not drawn to scale.
15
44) Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
5 ft
3 ft
9 ft
11 ft
18
45) You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft,
what will be the dimensions of your scale drawing?
46) Figure
. Name a pair of corresponding sides?
47) ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.
X
B
W
A
Zy
C
D
Z
48) Triangles ABC and DEF are similar. Find the lengths of AB and EF.
A
D
5x
5
E
B
4
x F
C
49) State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. If
not similar, write not similar.
a. ____________________________________
b. ______________________________________
50) Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the
diagram. What is the distance between the two campsites? The diagram is not to scale.
51) Find the length of the missing sides. Then determine the perimeter of the triangle.
52) Find the length of the missing side. The triangle is not drawn to scale.
25
24
53) You traveled 10 miles east and then 8 miles south. Exactly how far are you from your starting point?
54) Two students were asked to find the value of x in the figure. The equations they used are below. Decide whether
each student is correct or incorrect. If the student is incorrect, explain what they did wrong and then show the
correct equation. If the student was correct, write correct.
Lee’s equation:
𝑥
sin 57 = 15
Jamila’s equation:
15
cos 33 = 𝑥
55) Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
16
45°
Not drawn to scale
56) Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
x
y
30°
20
57) Write the tangent ratios for
and
.
P
29
21
R
Q
20
Not drawn to scale
58) A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a
249-foot-long shadow. Find the angle of elevation to the nearest degree. Draw a diagram to support your work!
59) Find the value of x. Round to the nearest tenth.
10

x
Not drawn to scale
60) A spotlight is mounted on a wall 17.4 feet above the ground in an office building. It is used to light an entrance
door 9.3 feet away. To the nearest degree, what is the angle of depression from the spotlight to the entrance door?
61) State whether the triangles are congruent. If so, write a congruence statement and the postulate or theorem you
used. If not congruent, write not congruent.
a. ____________________________________
b. ______________________________________
62) If ∆𝑫𝑳𝑸 ≅ ∆𝑬𝑴𝑹, then which of the following are not true?
a. LDQ  MRE
b. DLQ  EMR
c. RME  QLD
d. MRE  LQD
63) ∆𝑿𝒀𝒁 ≅ ∆𝑨𝑩𝑪. What angle is congruent to Y ?
64) Write the converse of the conditional statement: If it is raining, then the ground is wet.
65) Is the following a statement a good definition? Explain.
A square has four right angles.
66) Find a counterexample for the statement: If two shapes are similar, then they are congruent.
67) State the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot be proven
congruent, write not possible.
a) _________________
b) __________________
c) __________________
d) __________________
e) ___________________
f) ___________________
g) __________________
h) __________________
i) ___________________
j) ___________________
k) ___________________
i) ___________________
68) Name a pair of overlapping congruent triangles. State whether the triangles are congruent by SSS, SAS, ASA,
AAS, or HL.
69) Which two sides must be congruent to use ASA to prove DMX  JCX ?
70) Which two angles must be congruent to use SAS to prove ADX  CBX ?
71) Are the triangles congruent? If so, write a congruence statement and justify your reasoning. If not, write not
congruent.
72) Given: 𝑨𝑩 || 𝑫𝑪
𝑨𝑫 || 𝑩𝑪
Prove: ∆𝑨𝑫𝑪 ≅ ∆𝑪𝑩𝑨
73) Given: 𝑬𝑰 and 𝑯𝑭 bisect each other at G.
Prove:  E ≅  I
74) Given: MJ  JK
KL  ML
JK  ML
Prove: JM  KL
75) Given: ∆AED is isosceles
AB  CD
Prove: ∆BEC is isosceles
76) Find the area and perimeter of ΔABC.