Download Name: Period: ______ Geometry Unit 1: Tools of Geometry

Name: _______________________________________________ Period: _________
Unit 1: Tools of Geometry
Geometry
Homework
Section 1.1: Points, Lines, and Planes
Refer to figure 1 for questions 1 – 15.
1. Name AB in another way. 2. Give two other names for plane Q. 3. Why is EBD not an acceptable name
for plane Q?
Are the following sets of points and lines collinear? Why or why not?
4. AB and C
5. EB and A
6. B and F
7. F and plane Q
Are the following sets of points and lines coplanar?
8. E, B, and F
9. AC and ED
10. F, A, B, and C
11. Plane Q and EC
12. DB and FC
13. AE and DC
14. F, A, B, and D
Find the intersection of the following lines and planes in figure 2.
16. GK and LG
17. Planes GLM and LPN
19. Planes HJN and GKL
20. KP and plane KJN
Refer to figure 3 to answer questions 22 – 31.
22. Name plane P in another way.
15. FB and BD
18. Planes GHPN and KJP
21. KM and plane GHL
23. Name plane Q in another way.
24. Are A and C collinear?
25. What is the intersection of planes P and Q?
26. Are D, A, B, and C coplanar?
27. Are D and C collinear?
28. What is the intersection of AB and DC?
29. Are planes P and Q coplanar?
30. Are AB and plane Q coplanar?
31. Are B and C collinear?
REVIEW: Solve each equation.
1. 3x – 2 = 5(x – 15)
2. -4x + 7 = 6x – 23
3. -7x + 2(3x – 1) = -16 - x
Section 1.2: Segments, Rays, Parallel Lines and Planes
Is each statement true or false? Why?
1. XY is the same as YX.
2. XY is the same as YX.
3. If AB and AC are opposite rays, then they are collinear.
4. If two rays have the same endpoint, then they form a line.
5. If the union of two rays is a line, then the rays are opposite rays.
6. If PQ and PR are the same rays, then Q and R are the same point.
Use figure 1 to name each figure for questions 7 – 9.
7. all segments parallel to EF.
8. all segments parallel to FG.
Use figure 2 to answer questions 10 – 13.
10. Which pair(s) of planes is (are) parallel?
12. Which planes intersect in MN?
Use figure 3 to answer questions 14 – 19.
14. Name EF in another way.
9. three pairs of skew lines.
11. Which pair(s) of planes intersect?
13. Which planes intersect in RS?
15. How many different segments can be named?
16. Name GF in two other ways.
17. Name a pair of opposite rays with E as an endpoint.
18. Are EG and GE the same segment?
19. Name in two different ways the ray opposite FG.
REVIEW: Simplify.
1. 3/4 + 2/3
2. 7/8 – 2/3
3. 4 ½ + 3 ¼
4. 6 3/8 – 3 2/3
Section 1.3: Measuring Segments and Angles
Use figure 1 to find the value of each of the following in question 1 – 3 and use figure 2 for questions 4 – 6 if
GJ = 48 and AX = 27.
1. x
2. GH
3. HJ
4. y
5. AQ
6. QX
Use figure 3 for questions 29 – 30. Solve for x and find the angle measures.
7. ∠AOB = x + 3, ∠AOC = 2x + 11, ∠BOC = 4x – 7
8. ∠COD = 9x + 4, ∠BOC = 4x – 1, ∠BOD= 14x – 6
9. Name the angle in figure 4 in four different ways.
Name an angle or angles in figure 5 described by each of the following.
10. Complementary to ∠BOC
11. Supplementary to ∠BOC
13. Congruent to ∠AOD
12. Vertical to ∠EOD
14. Adjacent and congruent to ∠AOC
Use figure 6 for questions 15 - 23. Find the measure of each angle for question 15 - 20.
15. ∠EBF
16. ∠EBA
17. ∠DBE
18. ∠DBC
19. ∠ABF
20. ∠DBF
21. Name all acute angles
REVIEW: Simplify.
1. 3/4 ・7/9
22. Name all obtuse angles
2. 9/2 ÷ 6/5
3. 3 4/5 ・ 5 2/3
23. Name all right angles
4. 4 1/3 ÷ 2 1/2
Section 1.4: Geometric Figures
Classify each triangle by its sides and angles.
1.
2.
3.
4.
Classify each triangle in the figure by its sides and angles.
5. ∆ABD
6. ∆ABC
7. ∆EDC
8. ∆BDC
Describe what is shown in each diagram. Use correct notation.
9.
10.
12.
13.
11.
14.
Name each polygon. List any congruent or equal angles and sides.
B
B
15.
16.
17. A
A
50°
C
D
E
D
C
REVIEW: Simplify each radical to an exact answer.
1. √8
2. √28
3. √98
8 in
E
B
A
27 m
C
8 in
A
18.
50°
B
4. √200
D
C
5. √72
Section 1.5: Patterns, Ratios, and Proportions
Find a pattern for each sequence. Use the pattern to show the next two terms.
1. 17, 23, 29, 35, 41, …
2. 1.01, 1.001, 1.0001, …
3. 2, -4, 8, -16, 32, …
4. 1, 2, 4, 7, 11, 16, …
5. 12, 14, 18, 24, 32, …
Give a counterexample that disproves each conjecture.
7. No triangles have two sides of the same length.
9. Everyone who lives in Texas lives in Houston.
Solve each proportion.
11. x = 9
12. 6 = 2
4 3
x 11
13. 7 = x
5 3
14. 2 = x
x 32
6. 32, 48, 56, 60, 62, 63, …
8. If x2 = 16, then x = 4.
10. All cell phones have a touch screen.
15. 3 = 8
11 x
16. x = 3
x+2 4
18. Create 2 unique patters that consist of at least 3 different shape learned in section 1.4.
REVIEW: Let x = 3, y = -4, and z = 2. Evaluate each expression.
1. 3xy2
2. xy/z
3. ½xz
4. 2xy + 2xz + 2yz
17. x + 1 = 7
x
5
Unit 1 Review
Choose the correct term to complete each sentence.
1.  A ray that divides an angle into two congruent angles is a(n) __________________________.
2.  _________________________ are two lines that intersect to form right angles.
3.  _________________________ are two angles with measures that have a sum of 90.
4.  Figures that are in the same plane are _________________________.
5.  A(n) __________________ is the part of a line consisting of two endpoints and all points between them.
6.  Two segments with the same length are _________________________.
7.  A(n) __________________ of a segment is a point that divides the segment into two congruent segments.
8.  A(n) _________________________ is a ray that divides an angle into two congruent angles.
9.  A conclusion based upon inductive reasoning is sometimes called a(n) _________________________.
10.  A(n) _________________________ is an accepted statement of fact.
11.  _________________________ are coplanar lines that do not intersect.
12.  A(n) _________________________ is an angle whose measure is between 90 and 180.
Using figure 1, decide if each statement is
true or false.
13. A, D, F are coplanar.
14. A, B, E are coplanar.
15. A and C are collinear.
16. AC and FE are coplanar.
17. D, A, B, E are coplanar.
18. D, E, and B are collinear.
Use the figure 2 for exercises 19 - 24.
19. If BC = 12 and CE = 15, find BE.
20. What is the angle bisector of ∠ACB?
21. BC = 3x + 2 and CD = 5x – 10. Solve for x.
22. If AC = 5x – 16 and CF = 2x – 4, find AF.
23. If m∠BCG = 60 then find m∠GCA and m∠BCA.
24. If m∠ACD=60 and m∠DCH=20, then find m∠HCA.
Use the figure 3 for exercises 25 - 28.
25. What are two other ways to name AB?
26. What are two ways to name plane Q?
27. What are the names of three collinear points?
28. What are the names of four coplanar points?
Use the figure 4 for questions 29 - 31.
29. What are the names of the segments?
30. What are the names of the rays in the picture?
31. Which of the rays are opposite rays?
Draw each triangle with the following descriptions. Include side and angle measurements for each triangle.
32. An equilateral
33. An isosceles right
34. An obtuse scalene
35. An acute scalene
Solve each proportion.
36. x + 7 = 15
37. 9 = 3
7
5
5 x
38. 5 = 6
6 x
39. 2x – 1 = x
5
12
40. 5 = 10
x–3 x