SPRING STUDY GUIDE – Geometry Pre-AP
Well, this is it guys! We have made it to the end of our Spring semester together. As we prepare for our final exams, I
want to make it known that I believe that you all have the capacity to ace the Geometry Pre-AP exam. Make sure that
you are taking the final steps necessary to stay fresh on the concepts that we’ve learned the past few months. I hope
you all had a great school year, and let me know if you need any assistance. ~ Mr. Lacy
(FULL ANSWER SHEET WILL BE POSTED ON CLASS WEBSITE ON SUNDAY AFTERNOON – www.dallasisd.org/lacy)
Sum of Interior Angles of a Polygon
S = 180 (n – 2)
Interior Angle Measure of a Regular Polygon
* To find the interior angle measure of a regular polygon, divide the sum of the interior angles by the number of
sides of the polygon.
Exterior Angle Measure of a Regular Polygon
* To find the exterior angle measure of a regular polygon:
Exterior Angle = 180 – (Interior Angle Measure)
Triangle (3 sides), Quadrilateral (4 sides), Pentagon (5 sides), Hexagon (6 sides), Heptagon (7 sides), Octagon (8 sides),
Nonagon (9 sides), Decagon (10 sides), Dodecagon (11 sides)
Segments in Triangles
* A median is a segment that goes from a vertex to the midpoint (the middle) of the opposite side.
* An altitude is a segment that goes from a vertex to the opposite side and forms a right angle.
* A perpendicular bisector is a segment that forms a right angle at the midpoint of a side in a triangle. It does
not have to start at the vertex!
Slopes
* Slopes of parallel lines are the exact same.
* Slopes of perpendicular lines are opposite reciprocals. (They also multiply to give you – 1.)
Equations of Lines
* Slope-Intercept Form:
y = mx + b
[m is the slope, b is the y-intercept]
* Standard Form:
Ax + By = C
* Point-Slope Form:
y – y1 = m (x – x1)
[m is the slope, (x1, y1) is any point on the line]
Measurement
* Length, Width, Height are all measured in units.
* Area, Surface Area (Lateral and Total) are all measured in units2 or square units.
* Volume is measured in units3 or cubic units.
Scale Factor
* To find scale factor, use corresponding sides with the following formula:
1. List all of the properties of an isosceles trapezoid.
2. List all of the properties of a rhombus.
𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑁𝑒𝑤 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
𝑂𝑙𝑑 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡
3. Solve for x and find each side length.
3
x+2
2
x
4. Solve for x and find each side length.
x+6
14
x+3
7
5. Find the area of the composite figure.
6. Find the area of the shaded region.
7. How does the volume of a rectangular prism change if…
A) …the dimensions are reduced by a factor of 4?
B) …the dimensions are enlarged by a factor of 4?
C) …the dimensions are reduced by 4? (Think about the wording!)
8. Find the scale factor for each pair of figures.
9. The surface area of a small cylinder is 17π. The surface area of a large cylinder that is similar to the small one is 272π.
What is the scale factor for the two figures?
10. The surface area of a large cylinder is 1134π. The surface area of a small cylinder that is similar to the large one is 14π.
What is the scale factor for the two figures?
11. Find the volume of a rectangular prism that has a height of 300 ft, a length of 40 ft, and a width of 25ft. SHOW ALL
WORK AND FORMULAS!
12. Find the volume of a square pyramid that has a length of 40 ft, a width of 25 ft, and a height of 30 ft. SHOW ALL
WORK AND FORMULAS!
13. A building in the shape of a rectangular prism has 40 floors. Each floor is 12 feet high. The base of the building is 50 ft
long and 40 feet wide. The roof of the building is in the shape of a pyramid that is 20 ft high. What is the volume of the
entire building?
14. Find the exterior angle measure of a…
Nonagon
Decagon
Dodecagon
15. A marathon is 36 miles long. One mile is equal to 1609.34 meters.
Brother Bolt is practicing on a 400 meter long track. About how many times does he need to run around the track to
practice for a half marathon?
16. If the diameter of this circle is 17 cm, what is the probability of landing in each section?
Section A =
Section B =
Section C =
17. In this figure, YV = 7. Find the arc length of arc UY.
18. What is the midpoint of line segment AB if point A is (-5, 4) and point B is (9, -10)?
19. The slope of line m is 4. Write the slope of a line that is perpendicular to this line.
20. The slope of line r is
−1
2
, write the slope of a line that is perpendicular to this line.
21. Convert 2x + 4y = 12 to slope-intercept form.
22. Convert –3x – 2y = 10 to slope-intercept form.
23. Given the following figure, what is the probability of landing in each quadrant.
Quadrant 1 =
Quadrant 2 =
Quadrant 3 =
Quadrant 4 =
24. Brother X and Brother Y are standing 50 feet apart in a field. Brother X is flying his kite directly above Brother Y’s
head. If the string of the kite is 160 feet long and the handle is 4 feet off of the ground, how high is the kite above the
ground?
25. A 21 foot ladder is leaning against a building that is 15 feet tall. What angle does the ladder make with the ground?