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Geometry Essentials
REVIEW: Chapter 1
Name: ___________________________________
Use the diagram below for numbers 1 – 6.
1. Name 3 collinear points.
2. Name the plane in 2 different ways.
3. Give another name for line h.
4. Name the intersection of line h and line g.
5. �����⃗
𝑇𝑁 is opposite of what other ray?
6. Name the point that is non-coplanar with point N.
7. Point C is between A and B. If AC = 3.7 and AB = 12.4, find CB. (Hint: Draw a picture!)
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8. Solve for x and find the measures of ����
𝑅𝑆 and ��
𝑆𝑇
RS = 4x, ST = 12x, and RT = 128
( x2 − x1 ) 2 + ( y2 − y1 ) 2
R
S
 x1 + x2 y1 + y2 
 2 , 2 


9. Find the distance between the two points (−2, 7) and (0, −3).
10. Find the midpoint of a segment located with endpoints (3, −7) and (−1, −5).
T
�������⃗ bisects ∠𝑿𝒀𝒁.
Use the diagram to the right for number 11. 𝒀𝑾
11a) What does bisect mean?
11b) Put the correct markings on the diagram to indicate this.
11c) If 𝑚∠𝑋𝑌𝑊 = 75° , find 𝑚∠𝑋𝑌𝑍.
11d) Now assume 𝑚∠𝑋𝑌𝑊 = (4𝑥 + 15)° and 𝑚∠𝑊𝑌𝑍 = (6𝑥 – 5)°, find x and 𝑚∠𝑊𝑌𝑋.
Use the diagram to the right for number 12.
12a) The picture to the right is an example of what type of angles?
12b) If 𝑚∠2 = 40° , what is 𝑚∠1?
12c) Now if 𝑚∠2 = (2𝑥 + 7)° and 𝑚∠1 = (6𝑥 + 21)° , solve for x and find the measure of both angles.
Use the diagram to the right for number 13.
13a) Using the picture below, list two pairs of vertical angles.
13b) If 𝑚∠3 = 55° , what is 𝑚∠4?
13c) If 𝑚∠1 = (5𝑥 − 20)° and 𝑚∠2 = (4𝑥 + 8)° , solve for x and find the measure of both angles.
Use the diagram at the right for number 14.
14a) What does complementary mean?
M
N
14b) What is the value of x?
14c) What is the measure of ∠𝑀𝑄𝑁?
14d) What is the measure of ∠𝑃𝑄𝑁?
Q
P
Use the diagram to the right for number 15.
15a. What does supplementary mean?
15b. What is the value of x?
15c. Find the measure of the obtuse angle.
For numbers 16 – 21, use the formulas to assist you with finding the perimeter/circumference and area for each figure. Round
your answer to the hundredths place.
𝐴=
1
2
𝑏ℎ
𝐴 = 𝑏ℎ
𝐴 = 𝜋𝑟 2
𝐶 = 2𝜋𝜋
16.
17.
Perimeter:
Perimeter:
Area:
Area:
18.
19.
7.5 cm
7.5 cm
Perimeter:
Perimeter:
Area:
Area:
20.
21.
Circumference:
Area:
Circumference:
Area:
22. What is a concave polygon?
23. What is a convex polygon?
24. What is a regular polygon?
25. What is an irregular polygon?
For numbers 26 and 27, classify the figures by the number of sides, concave or convex, and regular or irregular.
26.
27.
Name: ____________________________
Name: _____________________________
Convex <or>
Concave
Convex <or>
Concave
Regular <or>
Irregular
Regular <or>
Irregular
28. Define the following words:
a) Acute
b) Right
c) Obtuse
29. Draw a picture of two angles that form a linear pair. What do we know about them?
30. Using the diagram below, list a pair of adjacent angles.
31. What does this symbol mean? ⊥ Define the word.
32. Draw a rough sketch of the final picture of each construction we did in class, showing all compass markings.
Bisect a segment
Bisect an angle
**You will not be asked to construct these on the test, but be able to recognize those markings for each type of construction.**