1

Geometry Formulas

Area Formulas

Lateral Area of cylinder 2C h rh Surface Area of prisms and cylinders 2LA B

Lateral Area of prism p h Surface Area of pyramids and cones LA B

Lateral Area of cone 1

2p r Surface Area of sphere

24 r

Lateral Area of pyramid 1

2p

2(Circle)A r (Triangle)

1

2A bh (Parallelogram)A bh (Regular Polygon)

1

2A ap

(Trapezoid) 1 2

1

2A b b h (Kite & Rhombus) 1 2

1

2A d d

Volume Formulas

Volume of prisms B h Volume pyramids1

3Bh

Volume of cylinders 2r h Volume of cones

21

3r h

Volume of sphere 34

3r

Other Formulas

2 2

2 1 2 1d x x y y 1 2 1 2,2 2

x x y y

2 2 2a b c

2C d r 2 1

2 1

y ym

x x

y mx b 1 1( )y y m x x

Special Right Triangles

3x

x

2x30

60

45

45

2xx

x

2

ACP GEOMETRY – MIDTERM REVIEW

Chapter 1 Review Questions

1. Find the next two terms in the sequence:

a) 384, 192, 96, 48,

b) -4, -8, 24, 48, -144,

c) ,256

1,

64

1,

16

1,

4

1

2. Which is the next figure in the sequence?

a) b) c) d)

e) None of the above

3. A B C

-5 10 x

If AC= 36, then x = ________

4.

-3 17

The distance between the two points is ______.

5. Identify what each of the following means:

a) AB b) ____

AB c)

AB d)

AB

3

6. Find a counterexample to show that each conjecture is false:

a) A number squared is greater than the number.

b) The difference of two positive integers is positive.

7. Use the figure to answer the questions:

a) Name two collinear points

b) Name two lines that intersect at point B.

c) Name three planes that intersect at point F.

d) Name two planes that do not intersect.

e) Name four points that are not coplanar.

f) Plane EFGH and

CH intersect at __________.

8.

T R U m

S

Y X V

a) Name a line segment.

b) Name a pair of opposite rays.

c) Name line m three different ways.

d) Name 2 lines which appear parallel.

9. a) M is a point on segment GS, b) G is the midpoint of

between G and S. segment LS.

GS = 32 LG = 6x+5

GM = 3x+10 GS = 2x +9

MS = x-2 Find x, LS, GS, LG

Find: x, GM, MS

4

1 2

T

JF K

10. a. Name 1 two other ways.

b. If m 1 = 142°, find m 2

c. KJT and TJF are ______________.

d. If m 2 = 5x+2 and m 1 = 24x+2, find x.

11. Use the points below to answer the following questions

A (0,3) B (-1, -4) C(-7.-9) D (8,10) E (0. -2)

Find: a) AE

b) BC

c) midpoint of segment BE

d) midpoint of segment CD

12. The midpoint of segment QT is (-5, 1). The coordinates of point Q are

(-7,4). Find the coordinates of point T.

13. Find the area of the region:

a) 6 b) Radius of larger circle = 4

Radius of smaller circle = 2

3

3

8

2

Find the area of the ‘donut’

14. Find the perimeter of a four sided figure with the following vertices:

A (-4, 5), B(3, 5), C(5, -2) and D(-4, -2).

5

Chapter 2 – Midterm Review

Identify the hypothesis and conclusion of each conditional statement.

1. If a figure is a rectangle, then it has four right angles.

2. If an integer ends with 0, then it is divisible by 5.

Write each sentence as a conditional

3. A square has four sides.

4. All obtuse angles have a measure greater than 90.

Show that each conditional is false by finding a counterexample.

5. If the name of a state contains the word New, then the state borders an ocean.

6. If an odd integer is less than ten, then the integer is prime.

Write the converse of each conditional statement, and determine the truth value of both statements.

7. If you are in Indiana, then you are in Indianapolis.

8. If a point is in the first quadrant, then its coordinates are positive.

Use the given property to complete each statement.

15. Addition Property of Equality: If 1052 x , then 2x = _____.

16. Subtraction Property of Equality: If 2165 x , then ______ = 15.

17. Symmetric Property of Equality: If AB = YU, then _____ = _____.

18. Symmetric Property of Equality: If KH , then _____ H .

19. Reflexive Property of Equality: PQR _____.

20. Distributive Property: 3( 1)x _____.

21. Substitution Property: If LM = 7 and EF + LM = NP, then _____ = NP.

22. Transitive Property of Congruence: If AOBXYZ and WYTAOB , then _____.

23. Multiplication Property of Equality: If UWTR 3

1, then _____.

6

If the conditional and its converse are true, write a biconditional statement.

24. If a point is a midpoint of a segment, then the point divides a segment into two congruent segments.

25. If two lines are parallel, then the two lines do not intersect.

Use the figure below to identify the following. (#30-34)

26. an angle supplementary to AOD

27. an angle adjacent AND congruent to AOE

28. an angle supplementary to EOA

29. an angle complementary to EOD

30. a pair of vertical angles

Find the value of the variables.

31. 32.

Chapter 3 Midterm Review 1) Find m1 and then m2. Justify each answer.

A B

C

D

EO

(7 3)x

(4 1)x 65(4 )y

(6 )y

7

2) Find the value of x. Then find the measure of each angle.

3) Find the value of x. Then find the measure of each angle.

5) Find the value of x for which a||t.

6) Find the value of x for which a||t.

8

7) Find the value of x for which a||t.

8) Find the value of x for which a||t.

9) Find the value of each variable.

9

10) Use a protractor and a ruler to measure the angles and sides of the triangle.

Classify the triangle by its angles and sides.

11) Find the values of the variables for the regular polygon below.

12) Find the missing angle measures

10

13) What is the interior angle sum of a convex 22-gon?

14) What is the measure of an exterior angle of a regular 13-gon?

15) The measure of an interior angle of a regular polygon is 135. Find the number of

sides.

Use the Coordinate Plane below to graph #16-18.

16) Graph 3x + 9y = 18 using slope-intercept form.

17) Graph x = -2.

18) Graph y = -5.

19) Write an equation of the line containing points A(2,7) and B(3,4).

11

21X

A

G

N

R

20) Are the lines parallel, perpendicular or neither? Explain.

y 3x 2

y 1

3x 2

Chapter 4

1) If ΔHIL ΔSUV name the corresponding angles and sides. (Sections 4-1)

2) Supply the reasons in this proof (Sections 4-2)

__ __

Given: X is the midpoint of AG and of NR.

Prove: ΔANX ΔGRX

Statements Reasons

__

a) X is the midpoint of AG

b) <1 <2

__ __

c) AX GX

__

d) X is the midpoint of NR

___ ___

e) NX RX

f) ΔANX ΔGRX

In 3 - 8 state which postulate, if any, could you use to prove the tow triangles congruent? If not enough

information is given, write not possible. (sections 4-2, 4-3, 4-6)

3) 4) 5)

12

6) 7) 8)

9 – 10 find the values of the variables (section 4-5).

9) 10)

y

x

110

50

x

y

100

11- 12) Prove using a two column proof or a paragraph proof. (Section 4-6 and 4-7)

11) __ __ __ __ __ __

Given: JL LM, LJ JK, and MJ KL

Prove: ΔMJL ΔKLJ

KM

J

L

13

12) __ __

Given: FE GH and <GHE <FEH

__ __

Prove: GE FH

M

F

E H

G

Chapter 6 1) A parallelogram is a quadrilateral with 2 pairs of .

2) A trapezoid is a quadrilateral with exactly 1 pair of .

3) A rectangle is a parallelogram with 4 .

4) A rhombus is a parallelogram with 4 .

5) A quadrilateral that is both a rhombus and a rectangle is called a ________.

Chapter 7

1. Find the value of h in the parallelogram.

Not drawn to scale

2. Find the length of the hypotenuse.

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3. The area of a square garden is 50 m2. How long is the diagonal?

4. Find the length, d, in simplest radical form, of the diagonal of a cube with sides of s units.

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

5.

6.

Find the area of the trapezoid. Leave your answer in simplest radical form.

7.

8. A kite has diagonals 9.2 ft and 8 ft. What is the area of the kite?

15

9. Find the area of the rhombus.

10. Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a

circle. Leave your answer in terms of .

Find the area. The figure is not drawn to scale.

11.

Find the length of the missing side. Leave your answer in simplest radical form.

12.