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Geometry Honors
Topic List for Midterm Exam t:.r,·
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The following is a list of topics that you may use to study for your Geometry Midterm. The topics are
listed in the same order that you learned each concept. Reviewing algebra skills such as factoring,
simplifying radicals, using quadratic formula and solving systems of equations are embedded in some
of the skills below! The sections in the book that relate to each topic are listed in parenthesis after
the topic.
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• Use notation to identify segments, rays, planes, lines. (1.1)
• Use Segment Addition Postulate (1.2)
• Use distance formula (leaving answers in simplest radical form). Identify congruent segments
using distance formula. (1.2/1.3)
• Use midpoint formula to find midpoint of segment . Use midpoint formula to find endpoint of
segment given one endpoint and the midpoint. (1.3)
• Find lengths of segments given the midpoint of a segment (1.3)
• Name and classify angles (1.4)
• Use the Angle Addition Postulate (1.4)
• Find measures of angles given an angle bisector (1.4)
• Perform congruence transformations (translations, reflections, and rotations) on the coordinate
plane (make sure you know the rules!!!) (4.8)
• Advanced reflections (know the rules for reflecting across the lines y = x, y = -x, and vertical and
horizontal lines) (9.3)
• Advanced rotations (know the rules for rotating about a point other than the origin) (9.4)
Unit 2:
• Find measures of complementary, supplementary, linear pairs, and vertical angles (1.5 and 2.7)
• Use Linear Pair Postulate, Vertical Angles Theorem, Congruent Complements Theorem and
Congruent Supplements Theorem to find measures of angles. (2.7)
• Identify angle pairs formed by two lines intersected by a transversal (corresponding, alternate
interior, alternate exterior, and consecutive interior angles) (3.1)
• Find measures of angles formed by paraliellines cut by a transversal (Corresponding Angles
Postulate, Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, and
Consecutive Interior Angles Theorem) (3.2)
• Prove lines are parallel using the Alternate Interior Angles Converse, Alternate Exterior Angles
Converse, Corresponding Angles Converse, and Consecutive Interior Angles Converse
• Complete Algebraic Proofs (3 .3)
• Complete proofs involving angle pairs formed by paraliellines cut by transversal (2.5 & 3.2 - 3.3)
• Find slopes of lines. (3.4)
• Use slope to determine if lines are parallel, perpendicular, or neither. (3 .5)
• Write equations of parallel and perpendicular lines (3.5)
Unit 3:
•
•
•
•
Classify triangles by side length and by angle measure (4.1)
Use Triangle Sum Theorem to find angle measures in triangles (4.1)
Use Exterior Angle Theorem to find measures of interior and exterior angles of triangles (4.1)
Use Properties of Isosceles and Equilateral Triangles to find angle measures and side lengths
(4.7)
• Classify Triangles on the coordinate plane using distance formula and slope formula (4.1 and 4.7)
• Congruent Triangle Proofs: SSS, SAS, ASA, AAS, HL and CPCTC (4.3, 4.4, 4.5, and 4.6)
Unit 4:
• Solve proportions. (6.1)
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Use extended ratios to solve problems (6.1)
Find the geometric mean of two numbers (6.1)
Use similar figures to find angle measures and side lengths (6.3)
Find perimeters of similar figures (6.3)
Find scale factors of similar figures (6.3)
Identify similar figures and write similarity statements (6.3)
Use AA~ to determine if triangles are similar (6.4)
Use AA~ with indirect measurement to find lengths (6.4)
Identify similar triangles using SSS~ and SAS~ (6.5)
Use Triangle Proportionality Theorems (Side Splitter Theorem, three parallel lines intersecting
two transversals proportionality theorem, and angle bisector proportionality theorem) (6.6)
• Perform dilations given a scale factor (6.7)
• Determine if a dilation is a reduction or an enlargement and identify scale factor (6.7)
• Perform dilations on the coordinate plane (centered at the origin and centered at a point other
than the origin) (6.7 and 9.7)
Geometry H Midterm Review Packet 2015-2016 1. Y..\ 'i
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CD has endpoint C(5,3) and 0(-8,9). To the nearest tenth, what is the distance, in units, from
point C to the midpoint of the segment?
2. ET has endpoint E(5,7) and midpoint M (2, -6). Find the coordinates for endpoint T.
3. BD bisects LABC. Find the value of x and m LABC .
4. If the mLABC= 88° then, solve for x.
A
B
5. Point"Mis between L and-o N on
LN . Use the given info'rmationto write an equation in terms of
x. Solve the equation. Then find LM and MN. LM = >i, MN= x and LN = 12.
6. A figure has vertices at A(l, -i), B(2,3), and C(4, -2) . After a transformation, the image of the
figure has vertices at A'(-l, -i), B'(-2, 3), and C' (-4, -2). Draw the preimage and image . Then
identify the transformation in words and in notation.
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7.
Find the coordinates for the image of llABe after the translation (x,Y)-7(x+2, y-l), then reflect
over the line y
=x.
Draw the image.
8. The figure shows part of a tile floor. Write the rule for the translation of hexagon 1 to hexagon 2. 9. The point A(4,3) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of the image? Find the coordinates of the image after the indicated composition of transformations.
10. YZ: Y(-2,4) and Z(-S,2) Reflection in x-axis; then rotation 90 about (-1,0) 0
11. YZ: Y(3,6) and Z (1,1) Reflection in y-axis; then rotation 180 about origin 0
2
12. The measure of an angle is 28° less than the measure of its complement. Find the measure of
the angle and the measure of its complement.
13. The measure of an angle is 12 less than 3 times the measure of its supplement. Find the
measure of the angle and the measure of its supplement.
14. Solve for x and y.
15. In this drawing, line p is parallel to line j and line t is perpendicular to AB . What is the measure
of L.BAC?
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17. Are these equations parallel, perpendicular, or neither?
1
b. q: 4x - 2y = 6
a. 1: y=-x-2 h:6y=2x+12
3
w: 2x+4y =6
18. Write an equation of a line which passes through P(-2, 5) and is perpendicular to the line
y=3x-7.
19. Given /11 m , find the values of x. Be sure to check for extraneous solutions. Diagram is not
drawn to scale.
a)
mL3=(x 2 +112)°, mL8=(16x+131)0
20. Given P lit, mL1 =(12x-4y)O, mL8 =(x-4y)o, and mL5=(15x+8y)o, find the values of x and
y, and the measure of each angle.
21. Find the value of x so that n
a.
II
m. State the theorem or postulate that justifiesyour solution.
b. m
c.
4
22. What values of x and y would make lines a and b parallel?
a
b
23. In
MBC,
mLA=(2x~5t,
mLB=(x-l)O,
and
mLC=(x+2t.
Classify the triangle by
its angles.
24. ~ARM, ~MAX, and ~XFM are all isosceles triangles. If
mLFXA = 96°, what is mLFMR?
X
25. a. Find the
mLACB
b. Find the
F
mLDBC
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A
c
26. Find the value of x
5
(3x + 10)"
27. Find the values of x and y.
28 . How are the interior angle of a triangle and its adjacent exterior angle related?
a. They are complementary angles
b. They are supplementary angles
c. They are congruent angles
d. They are vertical angles
29. Classify triangle XYZ according to its angle measures and side lengths.
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30. Given:AB.lBC, BD bisects LABC, mLABD = (x + 5y)O, mLDBC=(2x+2y+3)o.
Find the values of x and y.
A
B~---"'C
6
31. Given: DAIIYN; DA~YN
Prove:
LNDY ~ LDNA
Statements 1. 2. 3. 4. 5. Reasons
1.
2.
3.
4.
5.
32. Use the given information to write a proof. Prove : DB ~ CB o.........._ - " " i E - - - - nc
E
Statements Reasons
1. 1.
2. 2.
3. 4. 5. 3.
4.
5.
33. Given :
-- -- ---- -GH ~ KJ KG 1. GH and KJ 1. JH ­
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Prove: t.GHK ~ t.JKH
K~
Statements 1. 2. 3. 4. 5. ____
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Reasons
1.
2.
3.
4.
5.
7
34. Which of the following methods is NOT a method for proving triangle congruence?
a.SSS
b.SAS
c. AAS
d.SSA
35. If_3_ =?:, find the possible values of x.
x-4
7
36. Find the geometric mean of 15 and 9 in simplest radical form.
37. The measures of the angles of a triangle are in the extended ratio of 7:9:10. Find the measures of
the angles of the triangle.
38. The area of a rectangle is 294 yards 2 • The length and width are in the ratio of 3 : 2. Please find the
length, width, and perimeter of the rectangle.
39. The side lengths in ~ are related in an extended ratio of 7:10:14. Please solve for band c.
40. The hexagons below, ABCDEF and JKLGHI, are similar. If CD
=6, LG =9, and the perimeter of
ABCDEF is 40, what is the perimeter of JKLGHI?
I
L
D
H
G
8
41. A building casts a shadow 174 meters long. At the same time, a pole 5 meters high casts a shadow
15 meters long. What is the height of the building?
42. Michellewanted to measure the height of her school's flagpole. She placed a mirror on the ground
48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the
mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Please find the
height of the flagpole to the nearest tenth of a foot.
43. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on
the diagram. Assuming that the segments formed by
AB and FG are parallel, please explain why
the triangles are similar and find the distance between the two campsites?
Note: The diagram is not to scale.
44. Please solve for x.
a. b.
c.
x+s
9
45. In
MST, RS = 10, RT = 15, and mLR = 32°. In !1UVW, UV = 12, UW = 18, and mLU = 32° . Are
these triangles similar? If so, explain why and write a similarity statement.
46. Is a dilation by a scale factor of ~ an enlargement or a reduction? How can you tell?
47. Is a dilation by a scale factor of San enlargement or a reduction? How can you tell?
48. What are the coordinates of the polygon A(l,S) B(3,3) C(2, -6) D(-4, -2) after it is dilated by a
scale factor of 4?
49. What are the coordinates of the polygon A(-4,8) B(2,4) C(O,2) D( -4,6) after it is dilated by a
, scale
factor of~?
,
2
50. b.DEF has coordinates D(O, 5), E(4, 1) and F(2, 1); Please dilate the triangle using center (-1,2) and a
scaie factor 2.
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