Download Name Date I D C Geometry CP Midterm Review #1: Chapter 1

Name __________________________________________________________________ Date ______________________
Geometry CP Midterm Review #1: Chapter 1 - Tools of Geometry
I
D
Use the figure at the right to answer questions 1-8.
A
C
B
G
E
H
F
1. Name the intersection of plane ABFE and plane BCHF.
1. ____________________________
2. Name the intersection of ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐵𝐶 .
2. ____________________________
3. Name a pair of perpendicular segments.
3. ____________________________
4. Name a pair of parallel segments.
4. ____________________________
5. Name 3 collinear points.
5. ____________________________
6. Name 4 non-collinear points.
6. ____________________________
7. Name 4 coplanar points.
7. ____________________________
8. Name 4 non-coplanar points.
8. ____________________________
Classify each statement as true or false. If false, correct the statement to make it true.
9. Lines extend forever in two directions.
9. ____________________________
10. Planes have edges.
10. ____________________________
11. Any three points are collinear.
11. ____________________________
12. Through any two points, there is exactly one line.
12. ____________________________
13. Any three points are coplanar.
13. ____________________________
14. Any four points are coplanar.
14. ____________________________
15. The intersection of two planes is a point.
15. ____________________________
16. The intersection of two lines is a point.
16. ____________________________
17. Two lines that do not intersect are parallel.
17. ____________________________
18. If 𝐴𝑆 = 4𝑥 − 6, solve for x, then find BA and BS.
𝑥+4
𝑥+2
A
S
B
̅̅̅̅ ≅ 𝐴𝑇
̅̅̅̅ and 𝐴𝑇 = 3𝑐𝑚, what are AC and CT?
19. If 𝐴𝐶
C
T
A
20. ∠𝐴 and ∠𝐵 are supplementary angles. 𝑚∠𝐴 = 52°. What is 𝑚∠𝐵?
21. ∠𝑋 and ∠𝑌 are complementary angles. 𝑚∠𝑋 = (2𝑥 + 5)° and 𝑚∠𝑌 = (2𝑥 + 9)°. What is 𝑚∠𝑋?
22. If 𝑚∠𝐾𝐿𝑀 = (5𝑥 − 30)° and 𝑚∠𝑀𝐿𝑁 = (2𝑥)°, find the value of x AND the measure of each angle.
M
K
L
N
KEEP GOING!
23. ∠𝑃𝑄𝑅 and ∠𝑅𝑄𝑆 are congruent. If 𝑚∠𝑅𝑄𝑆 = 43°, what is the measure of ∠𝑃𝑄𝑆?
R
P
S
Q
24. ∠𝑋𝑌𝑍 is a right angle. If 𝑚∠𝑊𝑌𝑍 = (2𝑥)° and 𝑚∠𝑋𝑌𝑊 = (𝑥)°, find the value of x. Then find the measure of
each angle.
X
W
Y
Z
25. If Q is the midpoint of ̅̅̅̅
𝑃𝑅, and 𝑃𝑅 = 16, what is QR?
P
Q
R
26. If 𝑚∠1 = 2𝑥 + 10 and 𝑚∠3 = 50, find x and the measures of angles 2 and 4.
3
2
1
4
KEEP GOING!
Name __________________________________________________________________ Date ______________________
Geometry CP Midterm Review #2: Chapter 2 – Reasoning and Proof
For questions 1-8, match each statement with its appropriate property.
_______ 1. If
𝑥
3
= 5, then 𝑥 = 15
A. Addition Property
_______ 2. If 𝑥 + 10 = −21, then 𝑥 = −31
B. Division Property
_______ 3. If ∠𝑄 ≅ ∠𝑅, then ∠𝑅 ≅ ∠𝑄
C. Symmetric Property
_______ 4. If 𝑚∠𝐴 + 𝑚∠𝐵 = 180, and 𝑚∠𝐵 = 30, then 𝑚∠𝐴 + 30 = 180
D. Subtraction Property
_______ 5. If 5𝑥 = 10. Then 𝑥 = 2
E. Reflexive Property
_______ 6. ∠𝐵 = ∠𝐵
F. Substitution Property
_______ 7. If ∠1 ≅ ∠2, and ∠2 ≅ ∠3, then ∠1 ≅ ∠3
G. Multiplication Property
_______ 8. If 𝑧 − 15 = 30, then 𝑧 = 45
H. Transitive Property
9. Solve the following equation and indicate the property that justifies each step.
Given: 4𝑥 + 13 = 49
Statements
Reasons
A
M
10x
18+x
10. Given: M is the midpoint of AB
Solve for x
Statements
Reasons
1. M is the midpoint of AB
1.
2. AM  _____
2.
3. _________=18+x
4. 9x = _____
5. ___________
B
3.
4.
5.
Name __________________________________________________________________ Date ______________________
Geometry CP Midterm Review #3: Chapter 3 – Parallel and Perpendicular Lines
l || m
1
4
5
8
2
3
l
6
7
m
1. Name a pair of corresponding angles.
2. Name a pair of same-side interior angles.
3. Name a pair of alternate interior angles.
4. Name a pair of alternate exterior angles.
5. Name a pair of same-side exterior angles.
6. If 𝑚∠1 = 120°, what is the 𝑚∠5?
7. If 𝑚∠3 = 40°, what is the 𝑚∠6?
8. If 𝑚∠4 = 130°, what is the 𝑚∠6?
9. If 𝑚∠2 = 25°, what is the 𝑚∠5?
10. If 𝑚∠3 = 80°, what is the 𝑚∠8?
11. If 𝑚∠1 = (𝑥 + 50)°, and the If 𝑚∠8 = (𝑥 + 22)°,
what is the value of x and all of the angles?
12. If 𝑚∠4 = (3𝑥 + 20)°, and the If 𝑚∠6 = (2𝑥 + 30)°,
what is the value of x and all of the angles?
𝑥=
𝑥=
𝑚∠1 =
𝑚∠1 =
𝑚∠2 =
𝑚∠2 =
𝑚∠3 =
𝑚∠3 =
𝑚∠4 =
𝑚∠4 =
𝑚∠5 =
𝑚∠5 =
𝑚∠6 =
𝑚∠6 =
𝑚∠7 =
𝑚∠7 =
𝑚∠8 =
𝑚∠8 =
Refer to the diagram on the right for #13-19
1
5
13. Which angles are exterior angles?
14. What are the remote interior angles for ∠4?
15. What are the remote interior angles for ∠5?
16. What is the relationship between ∠2 and ∠5?
17. What is the relationship between ∠3 and ∠4?
18. If 𝑚∠2 = 60° and 𝑚∠1 = 45°, what is the 𝑚∠4?
19. If 𝑚∠3 = 60°, what is the 𝑚∠4?
20. If 𝑚∠5 = 120° and 𝑚∠3 = 75°, what is the 𝑚∠1?
21. Classify the following triangle by its sides and angles.
40°
10
10
70°
70°
2
3
4
Name __________________________________________________________________ Date ______________________
Geometry CP Midterm Review #4: Chapter 4 – Congruent Triangles
Determine if you can prove that two triangles congruent from the information given. If you can, say whether you can
prove it using SSS, SAS, ASA, AAS, or HL. If not, say it cannot be determined.
1.
2.
3.
4.
5.
6.
7. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹
̅̅̅̅ ≅ __________
𝐴𝐵
̅̅̅̅ ≅ __________
𝐴𝐶
̅̅̅̅ ≅ __________
𝐵𝐶
∠𝐴 ≅ __________
∠𝐵 ≅ __________
∠𝐶 ≅ __________
Solve for x in each of the following triangles.
8.
9.
x
5
9
60°
x
10.
11.
27°
x
(3x+5)°
Complete the following proofs.
̅̅̅̅ ≅ ̅̅̅̅
12. Given: 𝑆𝑅
𝑇𝑈;
̅𝑆𝑇
̅̅̅ ≅ 𝑅𝑈
̅̅̅̅
Prove: ∆𝑅𝑆𝑇 ≅ ∆𝑇𝑈𝑅
Statements
Reasons
̅̅̅̅ ≅ 𝑇𝑈
̅̅̅̅ ≅ 𝑅𝑈
̅̅̅̅; 𝑆𝑇
̅̅̅̅
1. 𝑆𝑅
1.
̅̅̅̅ ≅ 𝑅𝑇
̅̅̅̅
2. 𝑅𝑇
2.
3. ∆𝑅𝑆𝑇 ≅ ∆𝑇𝑈𝑅
3.
̅̅̅̅̅;
13. Given: N is the midpoint of 𝑀𝑃
N is the midpoint of ̅̅̅̅
𝐿𝑂
Prove: ∠𝐿 ≅ ∠𝑂
Statements
1. N is the midpoint of ̅̅̅̅̅
𝑀𝑃;
Reasons
1.
̅̅̅̅
N is the midpoint of 𝐿𝑂
2. ̅̅̅̅
𝑃𝑁 ≅ ̅̅̅̅̅
𝑁𝑀
2.
3. ̅̅̅̅
𝐿𝑁 ≅ ̅̅̅̅
𝑁𝑂
3.
4. ∠𝑀𝑁𝐿 ≅ ∠𝑂𝑁𝑃
4.
5. ∆𝑀𝑁𝐿 ≅ ∆𝑃𝑁𝑂
5.
6. ∠𝐿 ≅ ∠𝑂
6.
Separate and redraw the overlapping triangles. Identify any common angles or sides using tick marks. Name a pair of
overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
̅̅̅̅;
14. Given: ̅̅̅̅̅
𝑍𝑊 ≅ 𝑋𝑌
∠𝑌𝑋𝑊 and ∠𝑍𝑊𝑋 are right angles.
̅̅̅̅;
̅̅̅̅ ≅ 𝐿𝑂
15. Given: 𝐿𝑃
∠𝐿𝑂𝑀 ≅ ∠𝐿𝑃𝑁