Unit 1 Geometry Review

Segment and Angle Measurements (1.1)

100

LN = 45. Find x

     3x + 2                x +19 L_________M__________________N

    

x = 6

200

RS = 27. Find QS

             9x               12x-21

Q _____________R________S

RS = 63

300

Points L, M, and N are collinear. You are given LM = 13 and LN = 20. What is the value of MN? 

7

400

Ray BD bisects <ABC so that m<DBC = (x + 6) degrees and m<ABD = (2x - 12) degrees. What is <ABD?

24

500

Point K is located at 7 on a number line, and JK = KL. If the coordinate of L is 23, what is the coordinate of point J? 

-9

Distance & Midpoint (1.3)

100

Find the midpoint (leave as improper fraction):

(-3, 2) (1, 3)

(-1, 5/2)

200

Find the distance (leave as simplified square root):

(-3, 2) (1, 3)

Square root of 17

300

Find the distance (leave as simplified square root):

(1, 3) (5, 1)

2 square root 5

400

Find the distance between the following points: (1/2, 2) and (-3, -1/2). Leave answer as a decimal rounded to the nearest hundredth. 

4.30

500

Find the midpoint AND distance (leave as fraction or simplified square root):

(-3, 2) (1, -1)

Midpoint: (-1, 1/2) 

Distance: 5

Conditional Statements (1.5)

100

Write the converse of the conditional statement:

A number that is a multiple of 4 is a multiple of 2

If a number is a multiple of 2, then it is a multiple of 4

200

Write the inverse of the conditional:

If a number is a multiple of 4, then it is a multiple of 2

If a number is not a multiple of 4, then it is not a multiple of 2

300

Write the contrapositive of the conditional statement:

If a number is a multiple of 4, then it is a multiple of 2

If a number is not a multiple of 2, then it is not a multiple of 4

400

A cafeteria only offers pudding on Tuesdays. Use this fact to write a biconditional about the pudding

Pudding is available if and only if it is a Tuesday

500

Find the truth value of the conditional. Explain your reasoning or show a counterexample:

If a number is less than 4, then it is prime

FALSE: 1 is less than 4, but it is not prime

Inductive & Deductive Reasoning (1.4 & 1.6)

100

Find the next two terms:

1, 2, 6, 24, 120

720, 5040

200

If AB = BC, then DE = 2(AB). AB = 6 and BC = 6. What can you conclude?

DE = 12

300

Find a counterexample to disprove each statement, or support it with three examples:

If p is an even number, then p + 12 is even

True:

2 + 12 = 14

4 + 12 = 16

6 + 12 = 18

8 + 12 = 20

400

The table shows how much Jack saves in his bank account each week. At this rate, how much will he save on week 10?

Week             Savings ($)

1                        1.75

2                         3.50

3                         5.25

4                         7.00

$17.50

500

If it is a cloudy day, the water park is filled with less people. If the water park is filled with less people, the lines for each ride are short. Use the Law of Syllogism to write a true conditional

If it is a cloudy day, the lines for each ride are short.

Proofs (1.7 & 1.8)

100

If two angles are across from each other, we can use ________ to prove they are congruent

Vertical angles theorem

200

If two angles add up to 180 degrees, they are _______

Supplementary

300

It two angles (<2 and <3) are next to each other (on the same line), the statement "Angle 2 is supplementary to Angle 3" is justified by the ___________

Definition of a Linear Pair

400

Which could be the first step of an indirect proof of the conditional below? (Select all that apply - one by contradiction, one by contrapositive)

If x = 3, then 3x = x^2

1) If x = 3, then 3x = x^2

2) If 3x does not = x^2, then x does not = 3

3) Assume if 3x does not = x^2, then x does not = 3

4) Assume if x does not = 3, then 3x does not = x^2

2 & 4

500

Find the value of each vertical angle:

(3x - 6) = (2x + 22)

x = 28

angles = 78 degrees