Download Geometry CC Assignment #1 Naming Angles 1. Name the given

Geometry CC
Assignment #1
Naming Angles
1. Name the given angle in 3 ways.
A
2. Complementary angles are angles that add up to _______ degrees.
#1
3. Supplementary angles are angles that add up to _______ degrees.
4. Given rectangle ABCD. If m∠A = 4x − 10 , find x.
B
C
5. Given rectangle LMNO. If m∠N = x + 71 , find x.
6. Two angles are supplementary. If the larger angle is 16 degrees more than the smaller, find
both angles.
7. One angle is 20 degrees less than its complement. Find the measure of the larger angle.
8. One angle is 40 degrees larger than its supplement. Find both angles.
9 – 14: Solve for x.
9.
10.
A
11.
C
A
D
E
D
x + 40
x
x+10
B
C
B
C
13.
A
3x + 11
x + 10
A
B
12.
E
6x - 10
D
14.
V
A
Y
D
D
W
x + 20
x
x+ 3
x
B
C
m ∠ABC=64°
X
m ∠XWZ=2x + 4
m ∠VWX=7x - 13
E
Z
x
C
B
m ∠ABC=69°
R1. Solve for y: 0.4y + 1 = 0.35y + 0.2
R2. Factor: 3y 4 + 6y 3 + 9y 2
R3. Factor: 3x 2 + 14x + 8
R4. Evaluate: 3y −2 − x 3 , if y = 2 and x =
1
2
R5. Simplify: 3n 24n − 5 54n3
1.
2.
3.
4.
5.
6.
7.
∠B, ∠ABC, ∠CBA
90
180
25
19
82, 98
55, 35
8.
9.
10.
11.
12.
13.
14.
70, 110
20
40
7
22
21
22
R1. y = – 16
R2. 3y 2 y 2 + 2y + 3
(
R3.
( 3x + 2 )( x + 4 )
5
8
R5. −3n 6n
R4.
)
Geometry CC
Assignment #2
Parallel Lines #1
1 – 4: Use the diagram to the right. True or False?
1. ∠ 1 + ∠ 2 = ∠ 7 + ∠ 8
2. ∠ 3 + ∠ 1 = ∠ 6 + ∠ 8
3. ∠ 8 + ∠ 5 = ∠ 3 + ∠ 2
4. ∠ 1 + ∠ 3 = ∠ 7 + ∠ 5
2 1
3 4
7
6 5
8
5 – 10: Use the diagram to the right. True or False?
5. ∠ 1 & ∠ 4 are vertical angles.
6. ∠ 3 & ∠ 5 are corresponding angles.
7. ∠ 4 & ∠ 5 are alternate interior angles.
8. ∠ 1 & ∠ 7 are alternate exterior angles.
9. ∠ 3 & ∠ 5 are same side interior angles.
10. ∠ 5 & ∠ 6 are complementary angles.
1 2
3 4
5
6
7
8
11 – 16: Given m  n . Name the type of angles and determine whether the pairs are
supplementary or congruent.
11. ∠ 1 & ∠ 8
1
12. ∠ 2 & ∠ 6
2
3
5
4
6
13. ∠ 3 & ∠ 6
14. ∠ 5 & ∠ 8
15. ∠ 3 & ∠ 5
16. ∠ 2 & ∠ 8
7
8
m
n
17. a  b. Find x.
18. a  b. Find x.
a
3x
a
x - 20
x + 40
x
b
b
R1. Two complementary angles are represented by 2x and x + 15.
Find the measure of the smaller angle.
1
200 − 8
2
R2. Simplify: 4 50
R3. Simplify:
m2 − m − 30
R4. Simplify:
3m + 15
R5. Solve for x: 3(x – 1) = x – 13
1.
2.
3.
4.
5.
True
False
True
True
True
6. False
7. True
8. False
9. True
10. False
11. Alternate Exterior, Congruent
12. Corresponding, Congruent
13. Alternate Interior, Congruent
14. Vertical, Congruent
15. Same Side Interior, Supplementary
16. Same Side Exterior, Supplementary
17. x = 100
18. x = 20
R1. 40
R2. 20 2
R3. 3 2
m−6
R4.
3
R5. x = – 5
Geometry CC
Assignment #3
Parallel Lines #2
Solve for each angle. Show all work to justify your answer.
1. m∠a =_______
2.
3. m∠c =_______
4. m∠d =_______
5. x = ______
6. x = ______
m∠b =
_______
y = ______
7. x = ______
9. x = ______
8. x = ______
y = ______
10. x = ______
y = ______
y = ______
R1. Look up the definition of bisect and write it down.
R2. Look up the definition of linear pair and write it down.
R3. Solve for w:
1
w + 7 = 2w − 2
2
R4. Factor: − y 2 + 5y + 50
1.
2.
3.
4.
5.
a = 36
b = 47
c = 14
d = 49
x = 80
6.
7.
8.
9.
10.
x
x
x
x
x
=
=
=
=
=
30,
20
39,
80,
27,
y = 90
y = 123
y = 122
y = 47
R1.
R2.
R3.
R4.
Answer in class.
Answer in class.
w=6
− ( y − 10 )( y + 5 )
Geometry CC
Solve for each angle. Show all work to justify your answer.
1.
2.
3.
4.
5.
6.
7.
8.
Assignment #4
Unknown Angles 1
R1. Solve for y:
5
y−8 =
2
8
R2. If one angle of a triangle measures 90°, how are the other two angles related?
R3. Parallel lines that are cut by a transversal create pairs of angles that are equal in measure.
Name these pairs of angles.
R4. Define auxiliary line.
1.
2.
3.
4.
5.
6.
7.
8.
j = 92, k = 42, m = 46
n = 81
p = 18, q = 94
r = 46
a = 40
b = 48, c = 46
d = 50, e = 50
f = 82
R1. y = 16
R2. They must add to 90°
R3. Alternate interior angles, corresponding angles, alternate
exterior angles
R4. Answer in class.
Geometry CC
Assignment #5
Unknown Angles 2
Solve for each angle. Show all work to justify your answer.
Show calculations on a separate page.
1.
2.
3.
4.
5.
6.
7.
8.
R1. If – 2x + 3 = 7 and 3x + 1 = 5 + y, find the value of y.
R2. Solve for x: 5(2x – 7) = 15x – 10
R3. Solve for y:
y −3 6
=
3
y
R4. Solve for all missing angles.
1. c = 26, d = 31
5. h = 127
R1. y = – 10
2. e = 51
6. i = 60
R2. x = – 5
3. f = 30
7. j = 50
R3. y = 6, y = – 3
4. g = 143
8. k = 56
R4. b = d = 140, c = 40
Geometry CC
Assignment #6
Exterior Angle Theorem
Review: Isosceles and Equilateral Triangles
1 – 8: Solve for x. Show all work.
1.
2.
3.
4.
5.
6.
7.
Solve for ∠H .
8.
9.
In ∆ABC , with AC extended to D,
m∠BCD =
130 and m∠B =
20 .
What is m∠A ?
10. In the accompanying diagram of ∆ABC ,
AB is extended through D,
m∠CBD =
30 , and AB ≅ BC .
What is m∠A ?
Solve for ∠YDC .
R1. In ∆RST , ∠S is a right angle. The exterior angle at vertex S is
a) right
b) acute
c) obtuse
d)
straight
R2. Simplify: 5 20 − 2 45
R3. Factor: 2m2 − 11m + 9
R4. Factor: 5x 2 − 25x
1.
2.
3.
4.
5.
70
65
120
12
4
6.
7.
8.
9.
10.
3
38
140
110
15
R1. a
R2. 4 5
R3. ( m − 1)( 2m − 9 )
R4. 5x ( x − 5 )
Geometry CC
Assignment #7
Triangular Inequality
1 – 4: Tell whether the given lengths can be the measures of the sides of a triangle:
1. {3,4,5}
2. {5,8,13}
3. {6,7,10}
4. {3,9,15}
5 – 8: Find the range for the third side, s, of the triangle for each problem:
5. 2 and 4
R1.
6. 12 and 31
7. 9 and 4
8. 350 and 150
Simplify: 4 12
R2. Solve for x: x 2 − 6 =
x
R3. What does it mean for two lines to be coplanar?
R4. Two parallel lines are cut by a transversal forming alternate interior angles that are
supplementary. What conclusion can you draw about the measures of the angles formed
by the parallel lines and the transversal?
R5. Solve for d: 8d + 4 = 7d – 2(7 + d)
R6. The measure of an exterior angle at D of isosceles DDEF is 100. If DE = EF, find the
measure of each angle of the triangle.
1.
2.
3.
4.
5.
6.
7.
8.
Yes
No
Yes
No
2<s<6
19 < x < 43
5 < s < 13
200 < s < 500
R1.
R2.
R3.
R4.
R5.
R6.
8 3
x = {– 2, 3}
In same plane
Explain
d=6
80, 80, 20
Geometry CC
Assignment #8
Pythagorean Theorem
1. The hypotenuse of a right triangle is (always/sometimes/never) the longest side.
2. The 2 angles (other than the right angle) of a right triangle must be
(1) equal
(2) complementary
(3) supplementary
(4) obtuse
3. Name the formula that is used to determine the lengths of the sides of a right triangle.
4 – 7: Find x. Round your answer to the nearest tenth when necessary.
4.
5.
6.
7.
x
x
3
2
14
4
8
3
13
x
x
5
8.
Could {3, 6, 9} be the sides of a triangle? Show your work.
9.
Could {3, 6, 8} be the sides of a triangle? Show your work.
10. Could {7, 8, 12} be the sides of a RIGHT triangle? Show your work.
11. Could {15, 36, 39} be the sides of a RIGHT triangle? Show your work.
12. Could {2, 2 3 , 4} be the sides of a RIGHT triangle? Show your work.
13. Given ∆XYZ , where XZ ⊥ YZ . If XY = 17 and XZ = 15, find YZ.
14. Given ∆ABC , where AB ⊥ BC . If AC = 6 and AB = 2, find BC in simplest radical form.
15. Given ∆XYZ , where XY ⊥ YZ . Find YZ, if XZ = 10 and XY = 1.
R1. Given rectangle ABCD. If its perimeter is represented by 10x – 8 and AB = 3x – 5, express
as a binomial the length of BC.
R2. If the area of a rectangle is represented by x 2 − 9x + 14 and the length is represented by
x − 2 , express the width as a binomial.
R3. Given ∆ABC . If the ratio of ∠A to ∠B is 3:4 and ∠C is 10 degrees less than ∠A ,
find the measure of all three angles.
R4 – R6: Solve for x.
R4.
R5.
R6.
AB ⊥BC
m ∠ABD=3x-17
m ∠DBC=2x+2
2x+15
5x-17
2x-7
1.
2.
3.
4.
5.
6.
7.
Always
Complementary
Pythagorean Theorem
5
11.5
2.2
12
8.
9.
10.
11.
12.
13.
No, work
Yes, work
No, work
Yes, work
Yes, work
8
14. 4 2
15. 3
2x+7
R1.
R2.
R3.
R4.
R5.
R6.
2x + 1
(x – 7)
47, 57, 76
26
22.5
21
Geometry CC
Assignment #9
Ratio and Proportion
1.
Two numbers are in a 3:4 ratio. If their sum is 35, find both numbers.
2.
Two positive numbers are in a 1:3 ratio. If their product is 75, find both numbers.
3.
Two numbers are in a 7:4 ratio. If their difference is 33, find the numbers.
4.
Three numbers are in a 1:2:4 ratio. If their sum is 14, find all three numbers.
5.
Three numbers are in a 2:3:5 ratio. If 20 more than 3 times the smallest decreased by the
largest is equal to 14 more than the middle number, find the numbers.
6.
The measures of the sides of a triangle are in the ratio 5:6:7. Find the measure of each
side if the perimeter of the triangle is 72 inches.
7.
The length and width of a rectangle are in the ratio 5:8. If the perimeter of the rectangle is
156 feet, what are the length and width of the rectangle?
8.
Two supplementary angles are in a 1:5 ratio. What is the measure of the larger angle?
9 – 16: Find the value of each variable.
9.
x 1
=
8 2
10.
3x
=9
15
11. 6 =
13.
2x − 5
=x
3
14.
5p 2p − 4
=
3
2
15.
2x
5
12.
x + 5 x +1
=
4
3
y−4 1
=
9
3
16.
2x
+1 =
9
3
R1. Mr. Santana wants to carpet exactly half of his rectangular living room. He knows that the
perimeter of the room is 96 feet and that the length of the room is 6 feet longer than the
width. How many square feet of carpeting does Mr. Santana need?
R2. Find the area of the triangle to the nearest tenth of a square unit.
R3. The lengths of three sides of a triangle are 5, 7 and 8. Can it be a right triangle?
Show all work.
R4. Triangle RST is an isosceles right triangle with RS = ST and ∠ R and ∠ T are
complementary angles. What is the measure of each angle of the triangle.
R5. Can the sides of a triangle be represented by 3, 4, 4? Why or why not?
R6. In ∆ABC, m ∠ A = 74, m ∠ B = 58, and m ∠ C = 48. Name the shortest side of the triangle.
R7. If ∠ EFH is an exterior angle of ∆FGH, m ∠ EFH = 125, m ∠ G = 65, m ∠ H = 60, list the
sides of ∆FGH in order starting with the shortest.
1.
2.
3.
4.
5.
6.
7.
8.
15, 20
5, 15
77, 44
2, 4, 8
6, 9, 15
20, 24, 28
30, 48
30, 150
9.
10.
11.
12.
13.
14.
15.
16.
4
45
15
11
–5
–3
7
12
R1.
R2.
R3.
R4.
R5.
R6.
R7.
283.5
34.6
No, work
45, 45, 90
No, explain
AB
GH < GH< FH
Geometry CC
1.
Assignment #10
Similar Triangles 1
DABC  DDEF with m∠A = m∠D and m∠B = m∠E . Find the value of x.
a.
b.
c.
d.
A
AB = 8, BC = 10, DE = 16, EF = x
AB = 15, AC = x, DE = 3, DF = 5
AC = 24, BC = 32, DF = 8, EF = x
DE = 6, DF = 7, AB = 9, AC = x
D
E
B
C
2.
DEF and XYZ are similar right triangles where F and Z are the right angles and ∠D ≅ ∠X .
If DF = 3, EF = 4, and YZ = 8, find XY.
3.
The sides of a triangle are 3, 5, 6. The shortest side of a similar triangle is 12.
Find the perimeter of the second triangle.
4.
The sides of a triangle are 8, 10, 12. The perimeter of a similar triangle is 90.
Find the length of the longest side of the second triangle.
5.
The sides of a triangle measure 4, 9, 11. If the shortest side of a similar triangle measures
12, find the measures of the remaining sides of this triangle.
6.
The sides of a quadrilateral measure 12, 18, 20, 16. The longest side of a similar
quadrilateral measures 5. Find the measures of the remaining sides of this quadrilateral.
7.
Find the hypotenuse of an isosceles right triangle if a leg is 12.
8.
In ∆ABC , AB = 14 2 , m∠B =
45 , and m∠C =
90 . Find the area of ∆ABC .
R1.
What is the measure of the largest angle in the accompanying triangle?
R2.
The measure of an exterior angle at D of isosceles DDEF is 100°. If DE = EF, find the
measure of each angle of the triangle.
R3.
Simplify: 4 5 − 20
R4.
Factor: 4x 2 − 12x + 5
F
R5.
Factor completely: 3w 2 − 6w − 24
R6.
Given ∆XYZ , where XY ⊥ YZ . Find YZ, if XZ = 10 and XY = 1.
R7.
Solve for ∠YDC .
1.
2.
3.
4.
5.
6.
7.
8.
a. 20
b. 25
c. 10.6
d. 10.5
10
56
36
27, 33
3, 4, 5, 4
12 2
98
R1. 41, 56, 83
R2. 80, 80, 20
R3. 2 5
R4. (2x – 1)(2x – 5)
R5. 3(w – 4)(w + 2)
R6. 3
R7. 140
Geometry CC
Assignment #11
Similar Triangles 2
1.
In
a.
b.
c.
the diagram at the right, DE||AC.
AB = 24, BD = 12, BE = 15. Find BC.
AD = 10, BD = 8, BE = 12. Find BC.
AB = 20, BD = 9, BE = 18. Find EC.
2.
Given: ∆ABC  ∆XYZ with m∠A = m∠X and m∠B = m∠Y .
a. AB = 12, XY = 8, XZ = 16. Find AC.
b. BC = 40, AC = 50, XZ = 30. Find YZ.
3.
In the diagram at the right, AB  DE .
a. AB = 24, DE = 8, AC = 21. Find CE.
b. AC = 36, BC = 28, CE = 9. Find CD.
4.
In the diagram below, DD
ABC  DEF , with ∠A ≅ ∠D and ∠C ≅ ∠F . If AC = 18, BC = 24,
and DF = 12, find EF.
R1. The sides of a triangle are 6, 8, and 12. Find the length of the shortest side of a similar
triangle whose perimeter is 78.
R2. A boy 6 feet tall casts a shadow 24 feet long. At the same time, a nearby tree casts a 40
foot shadow. Find the number of feet in the height of the tree.
R3. Find the length of a leg.
R4. Find AB to the nearest 100th.
1. a. 30
b. 27
c. 22
2. a. 24
b. 24
3. a. 7
b. 7
4. 16
R1.
R2.
R3.
R4.
18
10
7 2
2.24
Geometry CC
Assignment #12
Ratios in Similar Figures - Area
1.
The ratio of the corresponding sides of 2 similar polygons is 2:3.
What is the ratio of their perimeters?
2.
The ratio of the corresponding sides of 2 similar polygons is 2:3.
What is the ratio of their areas?
3.
The ratio of the perimeters of 2 similar polygons is 4:9. What is the ratio of their areas?
4.
The ratio of the areas of 2 similar polygons is 9:25. What is the ratio of their perimeters?
5.
The ratio of the corresponding altitudes of 2 similar triangles is 5:8.
What is the ratio of their perimeters?
6.
The ratio of the corresponding sides of 2 similar triangles is 2:3. If the area of the smaller
triangle is 40, find the area of the larger triangle.
7.
The ratio of the areas of 2 similar triangles is 16:25. The perimeter of the larger triangle is
20. Find the perimeter of the smaller triangle.
R1. The ratio of the length to the width of a rectangle is 5:4. The perimeter of the rectangle is
72 inches. What are the dimensions of the rectangle?
R2. In right triangle ABC, m∠C = 3y − 10 , m∠B = y + 40 , and m∠A =
90 . What type of right
triangle is triangle ABC? Show all work.
(1) scalene
(2) isosceles
(3) equilateral
(4) obtuse
R3. Vertex angle A of isosceles triangle ABC measures 20° more than three times m∠B .
Calculate m∠C .
R4. Juliann plans on drawing ∆ABC, where the measure of ∠A can range from 50˚ to 60˚ and
the measure of ∠B can range from 90˚ to 100˚. Given these conditions, what is the
correct range of measures possible for ∠C ?
(1) 20˚ to 40˚
(2) 30˚ to 50˚
(3) 80˚ to 90˚
(4) 120˚ to 130˚
R5. Solve for x: 2x 2 + 2 =
5x
R6. Factor: 4x 2 − 16 .
R7. A tree 32 feet high casts a 20 foot shadow. Find the length of the shadow cast by a
nearby pole which is 24 feet tall.
1.
2.
3.
4.
5.
6.
7.
2:3
4:9
16:81
3:5
5:8
90
25
R1.
R2.
R3.
R4.
l = 20, w = 16
1, work
32
1
1
R5. x = , 2
2
R6. 4(x + 2)(x – 2)
R7. 15
Geometry CC
Assignment #13
Ratios in Similar Figures - Volume
1.
The ratio of the corresponding sides of 2 similar polygons is 2:3.
What is the ratio of their volumes?
2.
The ratio of the corresponding sides of 2 similar polygons is 4:5.
What is the ratio of their volumes?
3.
The ratio of the volumes of similar prisms is 64:343. What is the ratio of their sides?
4.
The ratio of the perimeters of 2 similar polygons is 4:9. What is the ratio of their volumes?
5.
The ratio of the area of 2 similar polygons is 9:25. What is the ratio of their volumes?
6.
The ratio of the corresponding altitudes of 2 similar triangles is 2:7. If the volume of the
smaller triangle is 24, what is the volume of the larger triangle?
7.
The ratio of the corresponding sides of 2 similar triangles is 2:3. If the volume of the
larger triangle is 108, find the volume of the smaller triangle.
8.
The ratio of the volume of 2 similar triangles is 8:27. If the area of the larger triangle is
54, find the area of the smaller triangle.
R1. Factor: 6x 3 y 8 − 9x 6 y 6 + 3x 2 y 4
x
8
=
3 x − 10
R3. Peach Street and Cherry Street are parallel. Apple Street
intersects them, as shown in the diagram below.
If m∠1= 2x + 36 and m∠2= 7x − 9 , what is m∠1 ?
R2. Solve.
R4. If ∆ABC ~ ∆XYZ , AC = 8, AB = 12, and XZ = 12, find the value of XY.
R5. The sides of a triangle are 3, 5, and 6. The shortest side of a similar triangle is 12.
Find the perimeter of the second triangle.
R6. In the diagram of ∆ABC below, DE C BC , AD = 3, DB = 2,
and DE = 6. What is the length of BC ?
1.
2.
3.
4.
5.
6.
7.
8.
8:27
64:125
4:7
64:729
27:125
1029
32
24
(
R1. 3x 2 y 4 2xy 4 − 3x 4 y 2 + 1
R2.
{−2, 12}
R3.
R4.
R5.
R6.
70
18
56
10
)
Geometry CC
1.
In
a.
b.
c.
d.
e.
f.
Assignment #14
Altitude to Hypotenuse 1
the diagram, right ∆ABC with altitude BD to hypotenuse AC.
AD = 2, BD = 4. Find DC.
BD = 6, DC = 9. Find AD.
AD = 1, DC = 25. Find BD.
AD = 2, AB = 6. Find AC.
DA = 1, DC = 15. Find AB.
A
AD = 9, DC= 16. Find BC.
B
C
D
N
2.
In the diagram, RT||MP. If NR = 3, TP = 4, and NT is one
more than RM. Find RM.
3.
The ratio of the corresponding sides of 2 similar polygons is
6:7. What is the ratio of their areas?
4.
The ratio of the edges of 2 cubes is 1:5. What is the ratio
of their volumes?
5.
The ratio of the corresponding sides of 2 similar triangles is 3:4. If the area of the smaller
triangle is 63, find the area of the larger triangle.
6.
The ratio of the areas of 2 similar triangles is 64:81. The perimeter of the larger triangle is
45. Find the perimeter of the smaller triangle.
7.
The sides of a triangle are 3, 4, and 6. If the longest side of a similar triangle is 60, find
the perimeter of the larger triangle.
R
M
x 2 − 100
R1. Reduce: 2
x − 6x − 40
R2. The length of a diagonal of a square is 4 2 inches. Find the length of a side of the
square and the perimeter of the square.
R3. Factor: 4c 2 − 25d2
R4. Solve for x: 3x – 2(5 – 2x) = 4
R5. If m∠1 =57 and ∠1 and ∠2 form a linear pair, find m∠2 .
R6. Simplify: 7 90
T
P
R7. Suppose that ∠1 ≅ ∠2 , m∠3= 4x + 30 , and m∠4 = 7x − 3 . Find the value of x.
3
1
2 4
R8. The measure of ∠ABC is 6 more than twice the measure of ∠EFG . The sum of the
measures of the two angles is 90˚. Find the measure of each angle.
1.
2.
3.
4.
5.
6.
7.
a. 8
b. 4
c. 5
d. 18
e. 4
f. 20
3
36:49
1:125
112
40
130
R1.
R2.
R3.
R4.
R5.
R6.
R7.
R8.
x + 10
x+4
4, p = 16
(2c + 5d)(2c – 5d)
2
123
21 10
11
28, 62
Geometry CC
Assignment #15
Altitude to Hypotenuse 2
1.
In right ∆ABC , altitude CD is drawn to hypotenuse AB.
a. AD = 3, CD= 9. Find DB.
b. AC = 10, AD = 2. Find DB.
2.
In right ∆ATC , altitude AP is drawn to hypotenuse TC.
a. TP = x, AP = 12, PC = x + 7. Find TP.
b. Find the area of ∆ATC .
3.
In right ∆SRT , altitude SW is drawn to hypotenuse RT.
a. RW = 10, WT = x, ST = 12. Find x.
b. Find SW to the nearest hundredth.
B
E
4.
In right ∆ABC , altitude CD is drawn to hypotenuse AB.
If AD = 5 and DB = 6, find CD in radical form.
5.
In the diagram to the right, AB  DE .
If BC = 10, CD= 15, and AC = 12, find CE.
C
A
D
R1. The area of a triangle is 48 and the height is 8. Find the base.
R2. Sterling silver uses a 37:3 ratio of silver to copper. How many grams of copper are in an
800 gram mass of sterling silver? [Hint: Sterling silver is the silver and copper together.]
R3. In right ∆ABC , AB = x, BC = x – 1, and AC = x – 8. Find x.
[Hint: Determine which expression is the longest side first.]
R4. A boy 6 feet tall is standing next to a girl who is 5 feet tall. The girl casts a shadow 90
inches long. Find the length of the boy’s shadow.
R5. The sides of a triangle are 8, 10, 12. The perimeter of a
similar triangle is 90. Find the length of the longest side of the
second triangle.
R6. Solve for x and y.
1. a.
b.
2. a.
b.
27
48
9
150
3. a. 8
b. 8.94
4. 30
5. 18
R1.
R2.
R3.
R4.
12
60
13
108
R5. 36
R6. x = 80,
y = 122
Geometry CC
Assignment #16
Angle Bisector Theorem
1. The sides of a triangle have lengths of 12, 16, and 21. An angle bisector meets the side of
length 21. Find the lengths of x and y.

2. The perimeter of ∆UVW is 22.5. WZ bisects ∠UWV , UZ = 2, and VZ = 2.5. Find UW and
VW.
3. The sides of a triangle have lengths of 5, 8 and 6.5. An angle bisector meets the side of
length 6.5. Find the lengths of both parts that make up the length of 6.5.
4. The sides of a triangle are 10.5, 16.5, and 9. An angle bisector meets the side of length 9.
Find lengths of the two parts that make up the length of 9.
5. In the diagram of DDEF below, DG is an angle bisector,
1
DE = 8, DF = 6, and EF = 8 . Find FG and EG.
6
6. Given CD = 3, DB = 4, BF = 4, FE = 5, AB = 6 and ∠CAD ≅ ∠DAB ≅ ∠BAF ≅ ∠FAE , find
the perimeter of quadrilateral AEBC. [Find the lengths of CA and AE first.]
R1. Three angles of a triangle are represented by 3x + 5, 2x – 7 and 2x.
What is the measure of the smallest angle of the triangle?
R2. A 20-foot pole that is leaning against a wall reaches a point that is 18 feet above the
ground. Find to the nearest degree, the measure of the angle that the pole makes with
the ground.
R3. Simplify:
125
R4. Given the diagram, ∠CAB ≅ ∠CFE . Find AB.
1.
2.
3.
4.
x = 9, y = 12
UW = 8, VW = 10
2.5 and 4
5.5 and 3.5
1
2
5. GE = 4 and FG = 3
2
3
6. CA = 4.5 and EA = 7.5, Perimeter = 28
R1.
R2.
R3.
R4.
45
68 degrees
5 5
7.5
Geometry CC
1.
Assignment #17
Centroid and Incenter
In ∆ABC , P is the centroid.
a)
b)
c)
d)
e)
f)
If
If
If
If
If
If
E
A
AP = 8, find PF.
EP = 6, find PC.
DP = 3, find DB.
AP = 4, find AF.
EC = 15, find EP and PC.
PF = 7, find AF.
P
F
D
C
C
1. In ∆ABC , m∠CAB =40° , m∠ABC =60° , and incenter P is drawn.
a)
b)
c)
d)
Find
Find
Find
Find
B
m∠BCA
the measure of each angle of ∆APB
the measure of each angle of ∆BPC
the measure of each angle of ∆CPA
M
P
A
N
Find
Find
Find
Find
the
the
the
the
measure
measure
measure
measure
of
of
of
of
each
each
each
each
acute
angle
angle
angle
B
A
2. Given isosceles right ∆ABC . Point P is the incenter.
a)
b)
c)
d)
L
angle of ∆ABC
of ∆APB
of ∆BPC
of ∆CPA
P
B
C
R1. In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If
the perimeter of the larger triangle is 32, find the perimeter of the smaller triangle.
(1) 8
(2) 16
(3) 21
(4) 28
B
R2. In the diagram of ∆ABC, AB = 10, BC = 14, and AC = 16. Find
the perimeter of the triangle formed by connecting the
midpoints of the sides of ∆ABC.
14
10
A
16
C
R3.
30 and m∠4 =
110 .
In the diagram, line L1 is parallel to line L 2 , m∠3 =
Find m∠2 .
C
L1
3 2 1
6
A
1.
a)
b)
c)
d)
e)
f)
4
12
9
6
5, 10
21
2. a) 80
3. a) 45, 45
R1. 4
b) 20, 30, 130
b) 22.5, 22.5, 135
R2. 20
c) 30, 40, 110
c) 45, 22.5, 112.5
R3. 80
d) 20, 40, 120
d) 45, 22.5, 112.5
5 4
B
L2
Geometry CC
Assignment #18
Trigonometry – Ratios and Calculator
B
1 – 2: For each triangle, find
a) tan A
b) cos A
c) sin A
1.
d) tan B
e) cos B
f) sin B
hypotenuse
opposite
C
adjacent to
A
2.
3 – 10: Solve for the missing side to the nearest hundredth.
3.
4.
5.
6.
7.
8.
Island Trees Math Department
9.
10.
R1. Given: a  b . Solve for x:
R2. AB // CD , FG bisects ∠EFD . If
m∠EFG = x and m∠FEG = 4 x , find
m∠EGF.
R3. Solve for x:
2
x − 7 =−3
5
R4. Factor: 8x 2 + 10x − 3
R5. If
50 + 18 =
x 2 , what is the value of x?
R6. Factor completely: 3x 2 + 6x − 45
a) tan A
1.
1
2.
5
12
3.
4.
5.
6.
47.06
17
35.62
9.08
b) cos A
3
c) sin A
3
18
12
13
18
5
13
7. 67.04
8. 14.43
9. 25.36
10. 63.09
d) tan B
1
12
5
R1.
R2.
R3.
R4.
R5.
R6.
e) cos B
3
f) sin B
3
18
5
13
18
12
13
130
30
10
(4x – 1)(2x + 3)
8
3(x + 5)(x – 3)
Island Trees Math Department
Geometry CC
Assignment #19
Trigonometry – Missing Angles
1 – 6: Solve for the missing angle to the nearest degree.
1.
2.
3.
4.
5.
6.
R1. Given: WX // YZ . If m∠CEW = m∠BEX = 50°, find m∠EGF.

R2. Given: BE ⊥ BD and ABC . Solve for x.
R3. Factor completely: 2 y 3 − 18 y
R4. Factor: 9 − 4n 2
R5. Solve for x: x 2 + ( x − 1) = ( x + 1)
2
2
R6. AB ⊥ BC , m∠A = 44° , m∠E = 21° .
Find m∠EDC.
1.
2.
3.
45
28
59
4.
5.
6.
17
83
74
R1. 50
R2. 40
R3. 2y(y + 3)(y – 3)
R4. (3 – 2n)(3 + 2n)
R5. x = 0, x = 4
R6. 113
Geometry CC
Assignment #20
Trigonometry – Verbal Problems
1.
A boy flying a kite lets out 392 feet of string, which makes an angle of 52° with the
ground. Assuming that the string is tied to the ground, find to the nearest foot, how
high the kite is flying above the ground.
2.
A ladder that leans against a building makes an angle of 75° with the ground and
reaches a point on the building 9.7 meters above the ground.
Find to the nearest meter the length of the ladder.
3.
Find to the nearest degree the measure of the angle of elevation of the sun if a child 88
centimeters tall casts a shadow 180 centimeters long.
4.
From an airplane that is flying at an altitude of 3,500 feet, the angle of depression of an
airport ground signal measures 27°. Find to the nearest hundred feet the distance
between the airplane and the airport signal.
5.
A 20-foot pole that is leaning against a wall reaches a point that is 18 feet above the
ground. Find to the nearest degree, the measure of the angle that the pole makes with
the ground.
6.
An airplane rises at an angle of 14° with the ground. Find, to the nearest hundred feet,
the distance the airplane has flown when it has covered a horizontal distance of 1,500
feet.
7.
From the top of a lighthouse 194 feet high, the angle of depression of a boat out at sea
measures 34°. Find to the nearest foot the distance from the boat to the foot of the
lighthouse.
8.
In a park, a slide 9.1 feet long is perpendicular to the ladder to the top of the slide. The
distance from the foot of the ladder to the bottom of the slide is 10.1 feet. Find to the
nearest degree the
measure of the angle that the
slide makes with the
ground.
R1. The measures of the angles of a triangle are in the ratio 2:3:4.
In degrees, what is the measure of the largest angle of the triangle?
R2. Triangle ABC shown below is a right triangle with altitude AD drawn to hypotenuse BC .
If BD = 2 and DC = 10, what is the length of AB ?
R3. In the diagram below of right triangle ABC, an altitude is drawn to hypotenuse AB .
Which proportion would always represent a correct relationship of the segments?
A.
1.
2.
3.
4.
309
10
26
7709
c z
=
z y
B.
c a
=
a y
5.
6.
7.
8.
64
1546
288
26
C.
x z
=
z y
D.
R1. 80
R2. 2 6
R3. C
y b
=
b x
Geometry CC
Assignment #21
Trigonometry – Advanced Verbal Problems
1.
At Mogul’s Ski Resort, the beginner’s slope is inclined at an angle of 12.3° , while the
advanced slope is inclined at an angle of 26.4° . If Rudy skis 1000 meters down the
advanced slope, while Valerie skis the same distance on the beginner’s slope, how much
longer was the horizontal distance that Valerie covered, to the nearest tenth?
2.
As shown in the diagram below, a ship is heading directly toward a lighthouse whose
beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation
from the ship to the light was 7° . A short time later, at point D, the angle of elevation
was 16° .
To the nearest foot, determine and state how far the ship traveled from point A to point
D.
3.
A sign is place on top of an office building 135 feet tall. From a point on the sidewalk
level with the base of the building, the angle of elevation to the top of the sign is 40°
and the angle of elevation to the bottom of the sign is 32° . Sketch a diagram to
represent the building, the sign and the two angles, and find the height of the sign to
the nearest foot.
4.
The 17th hole at the Rivershore Golf Course is 197 yards from the teeing area to the
center of the green. Suppose the largest angle at which you can drive the golf ball to
the left is 9° and to the right is 8° . What is the width of the green, to the
nearest yard ?
1.
81.3 meters
2. 582 feet
3.
46 feet
4.
58 yards
Geometry CC
In 1 –
a)
b)
c)
Assignment #22
Coordinate Geometry – Slope Formula
6, in each case:
Plot both points and draw the line that they determine.
State whether the slope is positive, negative, zero, or undefined.
Find the slope algebraically, to verify your answer to part b.
1. (0, 1) and (4, 5)
2. (1, – 5) and (3, 9)
3. (0, 0) and (– 3, 6)
4. (– 2, 4) and (– 2, 2)
5. (4, 2) and (8, 2)
6. (6, – 4) and (6, 1)
In 7 – 10, draw a line with the given slope, m, through the given point.
7. Passes through (2, 5) and m = 4
8. Passes through (0, – 6) and m = 0
9. Passes through (1, 5) and m = − 4
10. Passes through (0, 0) and m = 2
3
3
R1.
Solve for y: x + y = 3
R2.
The measures of the three angles of a triangle are represented by x, 3x, and x + 30.
Find the value of x.
R3.
68 and m∠y =
In the diagram: AB C CD , m∠x =
117 .
What is m∠z ?
R4.
Solve for y: 2x + 3y = 9
R5.
If the length of a rectangle is 5 and the width is 4.
What is the length of the diagonal?
R6.
Solve for the missing side to the nearest hundredth.
 
1. a) graph
b) positive
c) 1
2. a) graph
b) positive
c) 7
3. a) graph
b) negative
c) – 2
4. a) graph
b) undefined
c)
−2
0
5. a) graph
b) zero
c)
0
4
6. a) graph
b) undefined
c)
5
0
7 – 10: Answers in class
R1. y = – x + 3
R2. 30
R3. 131
2
R4. y =
− x+3
3
R5.
41
R6. 17
Geometry CC
Assignment #23
Coordinate Geometry – Point Slope Formula
Equation of a Line
1 – 9: Write an equation of the line which is being described.
You may write your answer in slope-intercept form (y = mx + b) or in point-slope form.
You only have to have one answer. All correct forms of the answer will be given.
1.
2.
3.
4.
5.
6.
7.
8.
9.
The
The
The
The
The
The
The
The
The
slope is 3 and the y-intercept is 12.
slope is 2 and the line passes through the point (5, 16).
line passes through the points (3, 7) and (9, 7).
line passes through the points (5, 6) and (5, 11).
line passes through the points (3, 7) and (6, 13).
line passes through the points (– 3, 9) and (5, 17).
line passes through the points (4, – 4) and (– 8, 8).
line passes through the points (3, – 1) and (– 1, 5).
line passes through the points (– 3, – 2) and (9, 4).
R1. Determine if the following could be sides of a right triangle: {8, 15, 16} Show all work.
R2. Graph the following line using slope and y-intercept: y = 2x + 1
R3. The base angle of an isosceles triangle measures 40°. Find the measure of the vertex
angle.
R4. Factor completely: 9x 3 − x
2
R5. Solve for x: x=
2x + 80
R7. Evaluate: 3x 2 − 17x + 20 , if x = 4
R8. Evaluate: 3x 2 − 17x + 20 , if x =
R6. Factor: 3x 2 − 17x + 20
R9. Solve for x:
2x − 7 3x + 5
=
3
5
5
3
1. y = 3x +12
2. y = 2x + 6
6. y = x + 12
y – 9 = 1(x + 3)
y – 17 = 1(x – 5)
3. y = 7
y – 7 = 0(x – 3)
y – 7 = 0(x – 9)
7. y = 5 – x
y + 4 = – 1(x – 4)
y – 8 = – 1 (x + 8)
4. x = 5 (only answer)
Do not write like
below. Never have
denominators of zero!
5
y − 6=
( x − 5)
0
5
y − 11=
( x − 5)
0
3
8. y − 5 =− ( x + 1)
2
3
y + 1 =− ( x − 3 )
2
5. y = 2x + 1
y – 7 = 2(x – 3)
y – 13 = 2(x – 6)
1
( x + 3)
2
1
y − 4=
( x − 9)
2
9. y + 2=
R1.
No
R2.
Graph
R3.
100
R4.
x(3x – 1)(3x + 1)
R5.
10, – 8
R6.
(3x – 5)(x – 4)
R7.
0
R8.
0
R9.
50
Geometry CC
Assignment #24
Coordinate Geometry – Parallel and Perpendicular Lines
1. Find the slope of line AB:
a)
2. a)
b)
c)
d)
e)
f)
A(– 2, 0), B(5, 21)
What
What
What
What
What
What
is
is
is
is
is
is
the
the
the
the
the
the
slope
slope
slope
slope
slope
slope
of
of
of
of
of
of
b)
a
a
a
a
a
a
line
line
line
line
line
line
A(– 1, – 1), B(– 9, 7)
which
which
which
which
which
which
is
is
is
is
is
is
c) A(12, 4), B(1, – 4)
parallel to the line y = 4x – 7?
parallel to the line y = – x + 3?
parallel to the line x + 4y = 10?
perpendicular to the line y = 4x – 7?
perpendicular to the line y = – x + 3?
perpendicular to the line x + 4y = 10?
3 – 6: Find the equation of the line through the given point and perpendicular to each line.
 1

3.  − , − 2  ; 2x + 7y = – 15
 2

1
− x −3
5. (7, 3); y =
3
4. (0, 0); – 2x + 4y = 12
6. (2, – 2); y = 1
y
R1. Graph the following line using slope and y-intercept:=
1
x − 3 . Show work!!
2
R3. The degree measures of the angles of a triangle are represented by x – 10, 2x + 20,
and 3x – 10. Find the measure of each angle of the triangle.
R4. Find the slope of the line determined by the points A(2, – 3) and B(– 1, 3).
89
R5. Solve for x: x 2 + ( x + 3 ) =
2
R6. Does the point (3, – 7) lie on the graph of y = 6x – 25?
R7. The length of a rectangle is 4 more than twice the width. The perimeter is 56.
Find the area of the rectangle.
1. a) 3
b) – 1
8
c)
11
2. a) 4
b) – 1
1
c) −
4
1
d) −
4
e) 1
f) 4
3.
=
y+2
7
1
x +  or

2
2
7
1
y
x−
=
2
4
4.
y= – 2x
5.
y – 3 = 3(x – 7)
6.
x=2
R1. Graph
R2. 20, 80, 80
R3. – 2
1.
R4.
{5, − 8}
R5. Yes
R6. 160
Geometry CC
Assignment #25
Coordinate Geometry – Midpoint and Centroid
1. Find the midpoint of AB:
a) A(7, 9), B(11, 1)
b) A(– 2, 6), B(4, 18)
d) A(6, – 1), B (– 6, – 7)
e) A(c, 5d), B(9c, d)
c) A(9, 3), B(10, 6)
2. Find (x, y) if M is the midpoint of AB.
a) A(1, 5), M(2, 6), B(x, y)
b) A(x, y), M(0, 0), B(3, – 5)
c) A(x, y), M(6, – 2), B(10, 1)
d) A(4, 7), M(2, 10), B(x, y)
3 – 8: Find the coordinates of each centroid, using any method taught in class.
If you are using a graphing method, your graphs must be shown as your work.
3. A(– 3, 3), B(3, – 3), C(3, 9)
6. M(– 6, 2), N(0, 0), P(0, 10)
4. D(1, 2), E(7, 0), F(1, – 2)
7. R(– 1, – 1), S(17, – 1), T(5, 5)
5. J(– 1, 1), K(3, 1), L(1, 7)
8. X(5, – 2), Y(– 1, 3), Z(2, – 10)
R1. What is the slope of a line which is perpendicular to the line y = – x + 3?
R2. The line passes through the points (3, – 1) and (– 1, 5).
R3. A ladder that leans against a building makes an angle of 75° with the ground and
reaches a point on the building 9.7 meters above the ground. Find to the nearest meter
the length of the ladder.
R4. Given rectangle ABCD. If m∠A = 4x − 10 , find x.
a
x - 20
R5. Simplify: 3n 24n − 5 54n3
x
R6. Find x when a  b .
1. a) (9, 5)
b) (1, 12)
c) ( 9.5, 4.5 )
d) (0, – 4)
e) (5c, 3d)
2. a)
b)
c)
d)
(3, 7)
(– 3, 5)
(2, – 5)
(0, 13)
3. (1, 3)
R1. 1
4. (3, 0)
R2. y − 5 =−
5. (1, 3)
6. (– 2, 4)
7. (7, 1)
8. (2, – 3)
R3.
R4.
R5.
R6.
3
( x + 1)
2
3
y + 1 =− ( x − 3 )
2
10
25
−3n 6n
x = 100
b