Homework Help for Geometry

. 

1. Given: Circle O, Chords: AB ||CD, Chords: DE ≈ CE, Arc AB = 48°, Arc BC = 16°,find Arc CD.

2.

Given: Circle O, diameter, marked perpendicular, Chord BC= 8, find x.

3.

Given: Circle O, diameter, marked perpendicular, Chord BC= 10, find x

4.

Given: Circle O, CD is diameter, Chord AB || CD. Arc AB = 74°, Find Arc CA.

Part B: Using your knowledge of complementary, supplementary vertical, and adjacent angles, identify the pairs of angles named in each figure. For example, in Figure #1 you are to identify the supplementary angles, which are:

>AFC and >CFB

>AFD and >DFB

>CFB and >BFD

>BFD and >DFA

>DFA and >AFC

In figure #2, identify all of the vertical pairs of angles,

In figure #3, identify all of the complementary pairs of angles,

In figure #4, identify all of the vertical pairs of angles,

And so on for numbers 5-10.

Part A: Classify each of the following lines as parallel, transversal or perpendicular.

Part B: Using your knowledge of complementary, supplementary vertical, and adjacent angles, identify the pairs of angles named in each figure. For example, in Figure #1 you are to identify the supplementary angles, which are:

>AFC and >CFB

>AFD and >DFB

>CFB and >BFD

>BFD and >DFA

>DFA and >AFC

In figure #2, identify all of the vertical pairs of angles,

In figure #3, identify all of the complementary pairs of angles,

In figure #4, identify all of the vertical pairs of angles,

And so on for numbers 5-10.

Identify each polygon and calculate the perimeter for each.

1. 

2. 

3. 

4. 

5. 

1. 

Given: Circle O, CD is diameter, chords: AB || CD. Arc AB = 68°, Find Arc CA

2. 

Given: Circle O, Chords: AB ||CD, Chords: DE ≈ CE, Arc AB = 48°, Arc BC = 16°,find Arc CD.

3. 

Given: Circle O, diameter, marked perpendicular, Chord BC= 8, find x.

4. 

Given: Circle O, diameter, marked perpendicular, Chord BC= 10, find x

5. 

Given: Circle O, CD is diameter, Chord AB || CD. Arc AB = 74°, Find Arc CA.

1. Solve for the missing angle measures.

Set 1 angles a and c are ? and are also ? Set 2 angles b and d are ? and are also ?

2.

set 1 angles a and c are ? set 2 angles b and d are ?

3.

angles a and b in both angles sets are ?

4.

Set 1 angle a = ?

Set 1 angle b = ?

Set 2 angle b = ?

Set 2 angle c = ?

5. Find the measure of each angle in the figure below.

Lines are named with the capital letter; angles are named with the lower case letter.

Angle a = ?

Angle b = ?

Angle c = ?

Angle d = ?

Angle e = ?

Angle f = ?

Find the volume of each pyramid with the given values.

1. A four- sided pyramid with base edge of 5 ft and h = 4 ft.

2. A four-sided pyramid with base edge of 10 ft and h = 7 ft.

3. A four-sided pyramid with base edge of 8 yds and h = 9 yds.

4. A four-sided pyramid with base edge of 20 ft and h = 15 ft.

5. A four-sided pyramid with base edge of 11 in and h = 20 in.

Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h=height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is…..

1. P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)

2. b = 4 in, P = 16 in, s = 12, 4 sides (base is a square)

3. P = 48 m, b = 12 m, s=12, 4 sides

4. P = 45 yds, b = 15 yds, s=15, h=12, 3 sides

5. b = 6 ft, P = 24 ft, s=6, 4 sides

6. P = 15 ft, b = 5 ft, s=5 ft, h= 4, 3 sides

7. b = 4 in, P = 16 in, s=11, 4 sides

8. P = 40 m, b = 10 m, s=10, 4 sides

9. P = 45 yds, b = 15 yds, s=10, h=8, 3 sides

10. b = 16 ft, P = 64 ft, s=8, 4 sides

11. b = 5 ft, P = 20 ft, s=7, 4 sides

12. P = 45 ft, b = 15 ft, s=10, h=8, 3 sides

13. b = 13 in, P = 52 in, s=11, 4 sides

14. P = 28 m, b = 7 m, s=8, 4 sides

15. P = 27 yds, b = 9 yds, s=30, h=25, 3 sides

1. 

2. 

3. 

4. 

5. 

1. 

Given: Circle O, CD is diameter, chords: AB || CD. Arc AB = 68°, Find Arc CA

2. 

Given: Circle O, Chords: AB ||CD, Chords: DE ≈ CE, Arc AB = 48°, Arc BC = 16°,find Arc CD.

3. 

Given: Circle O, diameter, marked perpendicular, Chord BC= 8, find x.

4. 

Given: Circle O, diameter, marked perpendicular, Chord BC= 10, find x

5. 

Given: Circle O, CD is diameter, Chord AB || CD. Arc AB = 74°, Find Arc CA.

1. Amy wants to her ice cream cone filled exactly to the top. The radius of the cone is 2 in. and the height is 6 in. How much ice cream will it take to fill the cone?

Note: As you can see, an ice cream cone is an upside down cone. This doesn’t change the formula…..

2. Jack is going to fill his beach ball with water. The radius of the ball is 24 in. How much water will it take to fill the beach ball?

3. Mary is sending her sister as summer camp a square box filled with tiny candies. The side of the box measures 6 in. How much candy will it take to fill the box?

4. Jim and Mary are competing in a math contest. They have to calculate how much it takes to completely fill a canister with a radius of 4 in. and a height of 5 in. with flour. How much flour will it take to fill the canister?

5. Aunt Lillian needs to fill a shoebox with packing material. The box measured 9 in by 5 in by 5 in. How much packing material does she need to fill the box?

(It doesn’t matter what the size, the formula stays the same….)

Identify the postulate for each drawing

1. 

2. 

3. 

4. 

5. 

Find the surface area of each of the following figures using the given values.

1. Cube: (s = side)

a. s = 5 ft b. s = 6 in c. s = 12 mm

2. Rectangular prism: ( l = length) (w = width) (h = height)

a. l = 2, w = 5, h = 7 (ft) b. l = 16 in, w = 11 in, h = 10 in

3. Sphere: (r = radius) (d = diameter)

a. r = 12 b. r = 16 c. d = 10

4. Cylinder: (r = radius) (h = height)

a. r = 6, h = 12 b. r = 2, h = 10 c. r = 3, h = 5

5. Application: Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?

Calculate the area of each of the polygons with the following dimensions.

1. Triangles

1. 1. B = 4in, H = 5in
2. 1. B = 6ft, H= 10ft
   2. B = 12m, H = 15m
   3. Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?

2. Parallelogram (H = height) and (B = base)

1. 1. H = 9in, B = 6in
2. 1. H = 5 ft, B = 2ft
3. 1. H = 7yds, B = 3yds
   2. Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?

Hint: Use the formula. Substitute the given values and then solve as an equation.

3. Rectangle (L = length) and (w = width)

1. 1. rect. DKIF with L = 8 ft and w = 6 ft
2. 1. rect. AOPU with L = 13 ft and w = 5 ft
   2. Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.

4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)

1. 1. rhombus with d1 = 12 yds and d2 = 12 yds
2. 1. rhombus with d1 = 10 ft and d2 = 25 ft
3. 1. rhombus with d1 = 16 in and d2 = 22 in
   2. Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?

5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)

1. 1. b1 = 6 ft, b2 = 7 ft, H = 10 ft
2. 1. b1 = 5 yds, b2 = 8 yds, H = 4 yds
   2. c. b1 = 9 in, b2 = 11 in, H = 13 in
   3. d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?

Hint: Use the formula. Substitute the given values and then solve as an equation.

Calculate the circumference of the circles with the following dimensions.
C = circumference
D = diameter
R = radius
PI = 3.14

1. a. D = 4 in

b. D = 6 in

c. D = 12 in
2. a. R = 2 ft

b. R = 14 ft

c. R = 12 ft
3. a. R = 9 ft

b. R = 11 ft

c. R = 7 ft
4. a. D = 10 ft

b. R = 9 ft

c. D = 13 ft
5. Application: Dana is planning to ride her bicycle around the circular race track and wants to know the distance. If the diameter of the track is 2 mile, how far is the distance around the race track?