Download Semester 1 Final Review

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Integrated Math 2 Semester 1 Final Review
CHAPTER 5 REVIEW
Find the measure of each numbered angle and name the
theorems that justify your work.
Find x so that l m. Identify the postulate or theorem you
used.
1. m 4 = 2x – 5
m 5 = 4x – 13
6.
2. m 1 = x + 10
7.
m 2 = 3x + 18
8.
3. m 6 = 7x – 24
m 7 = 5x + 14
9. STREETS Refer to the figure. Barton Road and Olive Tree
Lane form a right angle at their intersection. Tryon Street forms
a 57° angle with Olive Tree Lane. What is the measure of the
acute angle Tryon Street forms with Barton Road?
Given the following information, determine which lines, if
any, are parallel. State the postulate or theorem that
justifies your answer.
Determine whether the following statements are always,
sometimes, or never true. Explain.
10. The intersection of two planes contains at least two points.
4.
EFB
FBC
In the figure, m 2 = 92, and m 12 = 74. Find the measure
of each angle. Tell which postulate(s) or theorem(s) you
used.
5.
5
CHAPTER 6 REVIEW
Polygon ABCD
polygon PQRS.
1. Find the missing statement from the paragraph proof.
6. Find the value of x.
Given:
bisects
.
Find each measure.
Prove:
Proof:
Since it is given that
bisects
by the definition of an angle
bisector. It is given that
Property, ? . So
. By the Reflexive
by AAS. Therefore
by CPCTC.
7. m 3
Show that the polygons are congruent by identifying
all congruent corresponding parts. Then write a
congruence statement.
Find each measure.
2.
Refer to the figure below.
8. m 2
Find each measure.
3. If
, name two congruent angles.
Name the missing coordinates of each triangle.
4.
9. m 4
Refer to the figure below.
Determine which postulate can be used to prove that
the triangles are congruent. If it is not possible to
prove congruence, write not possible.
10.
5. If
, name two congruent angles.
CHAPTER 7 REVIEW
Use the Exterior Angle Inequality Theorem to list all
angles that satisfy the stated condition.
1. Use the figure below to determine the relationship
between EG and FG.
6. measures are greater than m 2
2. Find the measure of
In
, Z is the centroid, MZ = 6, YI = 18, and NZ =
12. Find each measure.
Use the figure below to determine which angle has
the greatest measure.
7. MR
Use the figure below to determine the relationship
between the measures of the given angles.
3.
1,
3,
4
8. m WQR, m QRW
In
, CP = 30, EP = 18, and BF = 39. Find each
measure.
Find the range for the measure of the third side of a
triangle given the measures of two sides.
9. 54 in. and 7 in.
10. SPORTS The figure shows the position of three trees
on one part of a disc golf course. At which tree position is
the angle between the trees the greatest?
4. PD
Is it possible to form a triangle with the given side
lengths? If not explain why not.
5. 2.7, 3.1, 4.3
CHAPTER 8 REVIEW
9. Find the sum of the measures of the interior angles of
a convex 30-gon.
1. What is
in kite STVW?
CHAPTER 9 REVIEW
ALGEBRA Identify the similar triangles. Then find
each measure.
The measure of an interior angle of a regular polygon
is given. Find the number of sides in the polygon.
1. NL, ML
2. 160
Determine whether each quadrilateral is a
parallelogram. Justify your answer.
3.
2. EG, HG
Quadrilateral GHJK is a rectangle. Find each
measure if m 1 = 37.
3. Find x and y.
4. m 6
ALGEBRA Quadrilateral RSTU is a rectangle.
5. If UZ = x + 21 and ZS = 3x – 15, find US.
Determine whether the dilation from A to B is an
enlargement or a reduction. Then find the scale
factor of the dilation.
Find the measures of an exterior angle and an
interior angle given the number of sides of each
regular polygon. Round to the nearest tenth, if
necessary.
6. 40
4.
Find the measure of each interior angle.
7.
8. For rhombus GHJK, find m 1.
Determine whether the triangles are similar. If so,
write a similarity statement. If not, what would be
sufficient to prove the triangles similar? Explain your
reasoning.
5.
ALGEBRA Find x.
4. An equilateral triangle has an altitude length of 33 feet.
Determine the length of a side of the triangle.
6.
Use a Pythagorean Triple to find x.
7. The ratio of the measures of the sides of a triangle is
3:4:6, and its perimeter is 104 feet. Find the measure of
each side of the triangle.
5.
Each pair of polygons is similar. Find the value of x.
Find x and y.
8.
Determine whether each pair of figures is similar. If
so, write the similarity statement and scale factor. If
not, explain your reasoning.
6.
Use a calculator to find the measure of
tenth.
to the nearest
9.
7.
CHAPTER 10 REVIEW
Find x, y, and z.
Find x.
1.
8.
Use a calculator to find the measure of
tenth.
to the nearest
Find the geometric mean between each pair of numbers.
9. 3 and 15
Determine whether each set of numbers can be measure
of the sides of a triangle. If so, classify the triangle as
acute, obtuse, or right. Justify your answer.
2.
10. 65, 72, 97
Find sin L, cos L, tan L, sin M, cos M, and tan M. Express
each ratio as a fraction and as a decimal to the nearest
hundredth.
3.
= 15, m = 36, n= 39
Ch. 5 Answer Key
Ch. 9 Answer Key
1. m 3 = 174, m 4 = 3, m 5 = 3, Supplement and Vertical
Angles Theorem
1.
; LN = 21; LM = 14
2.
; EG = 6; HG = 8
2. m 1 = 48, m 2 = 132, Supplement Theorem
3. m 6 = 109, m 7 = 109, Vertical Angles Theorem
4.
; Converse Alternate Interior Angles Theorem
5. 106; Consecutive Angles
6. 21; Alternate Exterior Angles
7. 9; Alternate Interior Angles
8. 12; Corresponding Angles
9. 33
10. Always; the intersection of two planes is a line, and a line
contains at least two points.
Ch. 6 Answer Key
1.
2.
3.
4. M(0, c), N(–2b, 0)
5.
6. x = 48
7. 65
8. 83
9. 45
10. SSS
Ch. 7 Answer Key
1. EG < FG
2. 19
3. angle 1
4. 15
5. yes
6. angle 6 and angle 9
7. 9
8. angle WQR < angle QRW
9. 47 in. < n < 61 in.
10. 2
Ch. 8 Answer Key
1. 130
2. 18
3. No; none of the tests for parallelograms are fulfilled.
4. 106
5. 78
6. 9, 171
7. m R = 128, m S = 52, m T = 128, m U = 52
8. 68
9. 5040
3.
4. enlargement; 3
5. yes;
by SAS Similarity
6.
7. 24 ft, 32 ft, 48 ft
8. 7
9.
;
Ch. 10 Answer Key
1. x = 15; y = 5; z = 17.3
2. 33.6 degrees
3. sin L = 0.38; cos L = 0.92; tan L = .42;
sin M = 0.92; cos M = 0.38; tan M = 2.4
4. 22 root 3 ft.
5. 52
6. x = 18; y = 9 root 3
7. 60.3 degrees
8. 105 root 2
9. 6.7
10. yes, right triangle.