Download Geometry Semester 1 Final Review

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Geometry Semester 1 Final Review
Chapter 1 Study Guide
Vocab: define in your
own words
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Adjacent angles
Angle bisector
Name_______________________
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Complementary
angles
Supplementary
angles
Congruent
Linear pair
Opposite Rays
Midpoint
1. Y is between X and Z. XY = 13.8, and XZ = 21.4. Find YZ (sketch it).
2. U is the midpoint of ̅̅̅̅
TV, TU=3x+4 and UV = 5x-2. Find TU, UV, and TV (sketch
it).
3. Classify each of the five possible angles as acute, right, or obtuse.
4. ⃗⃗⃗⃗⃗⃗
𝑁𝑃 bisects ∠𝑀𝑁𝑄, m∠𝑀𝑁𝑃 = (6𝑥 − 12)˚, and 𝑚∠𝑃𝑁𝑄 = (4𝑥 + 8)˚.
a. Draw a sketch of the angles
b. Find 𝑚∠𝑀𝑁𝑄.
5. Tell whether the angles are only adjacent, adjacent and form a linear pair, or
not adjacent.
a. ∠1 𝑎𝑛𝑑 ∠2
b. ∠3 𝑎𝑛𝑑 ∠4
c. ∠2 𝑎𝑛𝑑 ∠5
6. Find the measure of the complement and the supplement of each angle
a.
7. Find the midpoint of ̅̅̅̅
𝐴𝐵 with A(3,2) and B(-1, 4).
b.
X=18
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̅̅̅̅ with Q(-8,-5) and R(-4,7).
8. Find the midpoint of 𝑄𝑅
9. Use the Pythagorean Thm or the distance formula to find the distance
between X(3,-5) and Y(8,4).
10. Use the Pythagorean Thm or the distance formula to find the distance
between X(-2,4) and Y(6,1).
Constructions Study Guide
1. Copy ̅̅̅̅
𝑅𝑆
̅̅̅̅:
4. Perpendicularly bisect 𝑈𝑉
List the steps:
2. Copy ∠𝑇𝑅𝑆.
List the steps:
3. Construct a triangle congruent
to ∆RTS.
5. Construct an angle bisector for
∆RTS at ∠𝑇𝑅𝑆.
List the steps:
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Chapter 3 Study Guide
Vocab: define in your own words
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1.
Transversal
Alternate
exterior angles
Alternate interior
angles
Corresponding
angles
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Corresponding
sides
Parallel lines
Perpendicular
lines
Point-slope form
(linear equation)
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Identify the transversal and classify each angle pair:
a.
∠5 𝑎𝑛𝑑 ∠2
b.
∠6 𝑎𝑛𝑑 ∠3
c.
∠2 𝑎𝑛𝑑 ∠4
d.
∠1 𝑎𝑛𝑑 ∠2
2. Find 𝑚∠𝐷𝐸𝐹
3. Find 𝑚∠𝐴𝐵𝐶
4. Find 𝑚∠𝐾𝐿𝑀
5. Find 𝑚∠𝑄𝑅𝑆
Write the equation of each line in slope-intercept form.
6.
7.
8.
Same-side
interior angles
Slope
Slope-intercept
form (linear
equation)
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Write the equation of each line in the given form.
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9. The line with slope − 3 through (3, -1) in point-slope form.
10. The line through (-2, 2) and (4,-1) in slope-intercept form.
Use slopes to determine if the lines are parallel, perpendicular, or neither.
⃡⃗⃗⃗⃗
11.
𝐸𝐹 𝑎𝑛𝑑 ⃡⃗⃗⃗⃗
𝐺𝐻 for E(8,2), F(-3, 4), G(6, 1),
and H(-4, 3)
12. ⃡⃗⃗⃗
𝐽𝐾 𝑎𝑛𝑑 ⃡⃗⃗⃗⃗
𝐿𝑀 for J(4,3), K(-4, -2), L(5,6),
and M(-3, 1)
13. What is the equation in slope-intercept form of the line parallel to y=-3x+4 that goes through
the point (5,-2)?
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14. What is the equation in slope intercept form of the line parallel to 𝑦 = 4 𝑥 − 6 that goes through
the point (-8, 2)?
15. What is the equation in slope-intercept form of the line perpendicular to y=5x-7 that goes
through the point (10, 6)?
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16 What is the equation in slope-intercept form of the line perpendicular to 𝑦 = − 7 𝑥 − 6 that goes
through the point (8, -3)?
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Chapter 12 Study Guide
Vocab: define in your own words
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Transformation
Image and Pre-Image
Translation
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Reflection
Glide reflection
Line of symmetry
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Reflection
Rotational symmetry
1. Use the translation (𝑥, 𝑦) → (𝑥 + 3, 𝑌 − 3). Find the new set of coordinates and sketch.
2. Reflect the figure with the given vertices across
the given line.
a. E(-3, 2), F(0,2), G(-2, 5); reflect across xaxis.
b. P(6,4), Q(9, 4), and R(9,1); reflect across
y = x.
3. Translate the figure with the given vertices
along the given vector.
a. R(1, -1), S(1, -3), T(4, -3), U(4, -1);
translate {-5, 2}.
b. M(1, 4), N(4,4), P(3,1);
translate {3, 3}.
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4. Using the diagram below, reflect quadrilateral
ABCD over the line y = x. Label the vertices of
the image.
5. Using the diagram to the right describe the
rotation that carries MATH onto M’A’T’H’.
___________degrees
clockwise/counterclockwise (circle one)
6. Using the diagram to the right, write a rule
for the translation of ABCD to A’B’C’D’.
(𝑥, 𝑦) →
(_______ , ________)
7. Tell if each figure below has rotational
symmetry. If so, state the angle of rotational
symmetry and the order of symmetry.
a.
b.
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Chapter 4 Study Guide
Vocab: define in your own words
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Acute triangle
Base angle
CPCTC
Exterior angle
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Interior angle
Isosceles triangle
Equilateral
Obtuse triangle
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Right triangle
Equiangular
Scalene triangle
1. Find 𝑚∠𝑁 using the figure at right.
2. In ∆LMN, 𝑚∠𝐿 = 8𝑥˚, 𝑚∠𝑀 = (2𝑥 + 1)˚,
𝑎𝑛𝑑 𝑚∠𝑁 = (6𝑥 − 1)˚.
a. Sketch the triangle
b. Find 𝑚∠𝑁
3. ∆ABC ≅ ∆CDA
a. find x
b. find CD
4. Name all the 5 ways two triangles can be proven congruent. Choose two and draw an
example of each.
4. Given: 𝑚 ∥ l, and 𝑚∠𝐿𝑀𝐾 = 60°
Prove: m∠𝐺𝐹𝐻 = 120°
5.
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̅̅̅̅ ∥ 𝑄𝑃
̅̅̅̅ 𝑎𝑛𝑑 𝑁𝑂
̅̅̅̅ ≅ 𝑄𝑃
̅̅̅̅
6. Given: 𝑁𝑂
̅̅̅̅
̅̅̅̅
Prove: 𝑁𝑄 ≅ 𝑂𝑃
7.
∠𝑊 ≅ ∠𝑌
̅̅̅̅.
9. Find 𝑅𝑆
8. Find 𝑚∠𝐵 given 𝑚∠𝐴 = 3𝑡
and 𝑚∠𝐶 = 2𝑡 + 19
Chapter 5 Study Guide
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Vocab: define in your own words
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altitude of a triangle
median of a triangle
midsegment of a triangle
1. In ∆XYZ, find each measure
a. BC
b. XZ
c. 𝑚∠𝑌𝑋𝑍
d. 𝑚∠𝐵𝐶𝑍
2. Classify each triangle according to its side lengths and angle measures.
a. 9, 12, 16
b. 1.5, 3.6, 3.9
c. 3.7, 3.7, 4.1
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3. Find the value of x. Give your answer in the simplest radical form.
a.
b.
x
c.
4. A triangle has vertices A(11, 0), B(13, 12), and C(4,4). Find the equation of the
̅̅̅̅ .
median from vertex B to 𝐴𝐶
Chapter 6 Study Guide
Know the properties/conditions for each:
 Quadrilateral
 Parallelogram
 Rectangle
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Rhombus
Square
Trapezoid
1. Read each statement, then circle always, sometimes, or never true.
a. A rectangle is a rhombus.
Always Sometimes
Never
b. A trapezoid is a parallelogram
Always
Sometimes
Never
2. LKMN has coordinates L(-5,3), K(1,1), M(0,-2), and N(-6,0). Determine if it is any of the
following: a parallelogram, a rectangle, a rhombus, and/or a square.