Download 1. Find the next 3 numbers in the pattern: 3, -9, 27, -81

Geometry PreAP/GT
Chapter 2.1-2.6 Review
Name:
Date:
1. Find the next 3 numbers in the pattern: 3, -9, 27, -81,…
2. Find the first three numbers in the pattern: _____, _____, _____, 64, 128, 256,…
Sketch the next four figures in these patterns:
3.
4.
5. Distinguish between undefined terms, definitions, postulates, conjectures, and theorems.
6. Show the conjecture is false by finding a counterexample:
a. The sum of any two prime numbers is always even.
b. If the sum of two numbers is negative, then the two numbers must both be negative.
c. The sum of the measures of any two acute angles is the measure of an obtuse angle.
d. Each angle in a right triangle has a different measure.
7. Write the converse, inverse, and contrapositive of the conditional statement. Tell whether each statement is true
or false.
a. If a figure is a square, then it has four right angles.
b. If it is a bicycle, then it has two wheels.
c. If a point is the midpoint, then it bisects the segment.
8. Write the conclusion that follows from the true statements given.
a. If a triangle is obtuse then it has two acute angles. Two of the angles of ΔABC are 35° and 42°.
b. If Joe is in Antarctica, then the he sees penguins. Joe sees penguins.
c. If a person is not involved in student government, then she is not on Student Council. Ling is not on Student
Council.
d. If a person is not from the West Coast, then they are not from California. Julie is not from the West Coast.
̅̅̅̅ at point M.
̅̅̅̅ is the segment bisector of 𝐵𝐶
e. 𝑋𝑌
9. Write the conclusion. Assume the statements are true.
a. If two segments intersect, then they are not parallel. If two segments are not parallel, then they may be
perpendicular.
b. If you have a horse, then you have to feed it. If you have to feed the horse, then you have to get up early every
morning. If you get up early every morning, then you are tired at school.
c. If a person is driving over the speed limit, then the police officer will give them a ticket. If the police officer gives
them a ticket, then they will pay a fine.
10. Write each statement as a biconditional. What 2 statements must be true in order to write a biconditional
statement?
a. A cube is a three-dimensional solid with six square faces.
b. A right triangle is a triangle that contains a right angle.
c. B is between A and C when AB + BC = AC.
11. Decide whether the statement is true or false. If it is false, correct the statement by providing a counter example.
a. Through any two points, there exists exactly one line.
b. Through any two points, there exists exactly one plane.
c. A line can be in more than one plane.
d. If two planes intersect, then their intersection is a point.
12. Solve the equation for x. Write a reason for each step. (2 column proof)
a. 7(x – 4) + 3y = 4x – 1
b.
5(𝑥+4)
𝑥−2
= 35
13. Use the given property to complete the statement.
a. Symmetric Property of Equality: If MN = UY, then ____________.
b. Division Property of Equality: If 4(mQWR) = 120, then ________________.
c. Transitive Property of Equality: If SC = VT and ____________=MN, then __________________.
d. Addition Property of Equality: If y – 15 = 36, then _____________.
e. Reflexive Property of Equality: JL = ___________________.
14. Find the value of the variables.
a.
b.
(9x + 1)°
2(y + 15)° (4y −2)°
23)°
15. Use the picture to decide if the following statements are true or false.
A. Through points A, B, and D, there exists exactly one plane.
B. Through points D, B, and E, there exists exactly one plane.
C. Through points A and E, there exists exactly one line.
D. Line AE lies in plane AFE.
E. Points B and E are the intersections of line AB and line DE.
(13x − 51)°