Pre-AP Geometry 1st Semester Exam Study Guide

1) Name the intersection of plane DAG and plane ABD.

(left side and back) AD

2) Name the intersection of HI and FJ

E

3) Describe the relationship between the lines:

A) DC and FE parallel

B) GH and BC skew

C) HE and EC intersecting

4) Find the value of the variable and YZ if Y is between X and Z. XY = 2c +1, YZ = 6c, XZ = 9c – 1

2 1 6 9 18 1 9 1

2

XY YZ XZc c c

ccc

66(2)12

YZ cYZYZ

5) Find the coordinates of T given that M is the midpoint of KT. K(10, -2) M(2, -12)

OR

10 2(2, 12) ,

2 2

10 22 12

2 2

4 10 24 2

6 22

x y

x y

x y

x y

6) Find mA if mA is 30 less than 2 times its supplement.

OR

7) Write the equation of a line, in slope-intercept form that passes

through (1, –4) and has a slope of -2.

2( 1) 4

22 42

2y xy xy x

8) Write an equation in point-slope form parallel to y = 3x + 2 and passes

through (6, 5).

Parallel lines have the same slope. Slope of y = 3x + 2 is 3,

so slope of line parallel is also 3. 3( 6) 5y x

9) Describe the relationship between the line that passes through (6, 8)

and (2, 11) and the line that passes through (1, 3) and (–3, 6).

Slope for (6, 8) and (2, 11) 11 8 3

2 6 4m

Slope for (1, 3) and (–3, 6) 6 3 3

3 1 4m

Slopes are the same therefore the lines are parallel.

2(supp) 302(180 ) 30360 2 30

3 330

110110

m Ax xx xx

Axm

2 30supp2 30 1803 210

702(1

70) 310

0

m A xx

x xx

xm Am A

Give the slope and y-intercept and graph the line.

10) y = 4x – 1 11) 2x + 3y = 6

12) y = x 13) x = –2 14) y = 4

m = 4, b = -1 2

3

A

Bm

2

6

3

C

Bb

Or 1 0y x

m = 1, b = 0

Vertical line Slope = undefined No y -intercept

Or 0 4y x

m = 0, b = 4 horizonal line

15) Determine the next item in the sequence.

A) 1, 2, 4, 7, 11, … 16 (add 1, add 2, add 3, add 4, so add 5)

B) 2, –4, 8, –16, … 32 ( multiply by -2)

C) 32, 8, 2, ½, … ⅛ (divide by 4 or multiply by ¼ )

16) Make a conjecture about each value or geometric relationship.

A) 1 and 2 are vertical angles 1 2 (vertical angle thm)

B) 3 and 4 are a linear pair 3supp 4 (linear pair post.)

#17 and #18: Find a counterexample.

17) If a number is divisible by 10, then it is divisible by 20.

One example: 30 is divisible by 10, but not by 20.

18) The quotient of two whole numbers is always a whole number.

One example: 5 divided by 8 is not a whole number.

Find the converse, inverse, & contrapositive.

19) “If it is payday, then I will get ice cream.”

Converse: If I will get ice cream, then it is payday.

Inverse: If it is not payday, then I will not get ice cream.

Contrapositive: If I will not get ice cream, then it is not payday.

Determine if the final statement is a valid conjecture. If so, write valid. If not, write invalid. 20) If you have a part time job, you work 20 hours a week. Joey has a part time job. Joey works 20 hours a week. Valid by law of detachment

21) If you have a part time job, then you work 20 hours a wk. If you work 20 hours a wk, then you will fall asleep in class. Monica has a part-time job Monica will fall asleep in class. Valid by law of syllogism

22) Make a truth table for: ( )p q p

p q p ( )q p ( )p q p

T T F T F T F F T F F T T T T F F T F F

Using the given statements, determine what property is used for the

final statement

24) 1. If 2x + 19 = 27.

2. 2x = 8

Subtraction property

25) 1. 12 = 2x + 8

2. 2x + 8 = 3y

3. 12 = 3y

Transitive or

substituion

23) 1. 7(x – 3) = 35 2. 35 = 7(x – 3) symmetric

Find the measure of each numbered angle.

27) m7 = 3x - 15, m5 = 2x

28) m4 = 3(x – 1), m5 = x + 7

26) m1 = x, m2 = x – 6

1 2

3

1 48, 2

1 2 906 90

2

42

6

3

48

90

9

m mx xx

xm mm

4 5 180 ( )3( 1) 7 1803 3 7 1804 4 180

4 3(44 1) 129

4 1764

5 44

4

7 51

m m linear pairx x

x xxx

xmm

4

5

5 6 7 8

7 3(15) 15 305 2(15) 306 8 180 30 150

7 5 ( . )3 15 2

15m

m m vert angle

m

s

m

x xx

m

Write a two-column proof

29) Given: ABC and DBE are vertical angles.

Prove: x = 15

STATEMENTS REASONS 1) Given 2) ABC DBE Vertical angle theorem

3) m ABC m DBE Def of

4) 5x – 10 = 3x + 20 Substitution 5) 2x – 10 = 20 Subtraction property 6) 2x = 30 Addition property 7) x = 15 Division property

30) Given: B is the midpoint of AC

C is the midpoint of BD

Prove: AB CD Statements Reasons 1) Given

2) AB BC . BC CD Def. of midpoint

3) AB CD transitive

Describe the relationship:

31) 12 and 1 alt. exterior

32) 3 and 6 same side int.

33) 4 and 10 alt. interior

34) 1 and 8 alt. exterior

35) 5 and 7 vertical angles

36) 3 and 4 linear pair angles

5x - 10

3x + 20

A B

C

D E

1 2 3

4

9 10

11 12 8 7

6 5

Find the value of x that will allow you to prove JK // LM

37) 38)

3 13 130 1803 117 1803 6

213

xxx

x

2 29 872 58

29x

xx

39)Classify ABC by the length of its sides if AB = 8, BC = 8, and AC = 10.

2 sides are congruent, therefore isosceles

40) Classify the triangle with angles measuring 97°, 63°, and 20°.

one angle is greater than 90, therefore obtuse.

41) Two sides of a triangle have sides 6 and 18. Find the range of the

length of the third side.

18-6 = 12 and 18 + 6 = 24 therefore 12 < x < 24

42) What is the measure of angle x?

59 9

31

0x

x

or

59 90 180

14

31

9

x

x

x

(3x – 13)°

130°

J K

M L

87°

(2x + 29)°

J K

M L

59°

x

43) Find the values of x and y. (angles across from sides are )

180 102

78

y

y

2 180

2(78) 180

156 180

24

x y

x

x

x

y

44) Complete the congruence statement. EFG ≅ HIJ

45) Find the value of x and m2 if RL is an altitude of RTU,

m1 = 6x – 3 and m2 = 7x + 2

since RL is an altitude, then RT TU

1 2 906 3 7 2 9013 1 9013 91

7 2 1( )2 577

m mx xxx

xm

46) If RS in an angle bisector of RTU, and mURS = 2x – 5 and mTRS =

x + 15, find the value of x and mURT.

2 5 15

2( )2(20 15)

20

70

m URS m TRSx x

m URx

mT TRST

mUR

47) Find the value of x. 32

32 32 18064116

180x

xx

48) Find the value of x.

Since angles are congruent, then sides are congruent.

So 9x-7 = 4x+8 = 6x+2. Just use any two of these.

4 8 6 28 2 263

2

x xx

xx

49) Are the triangles congruent? If so, state theorem used.

No, you only know about one pair of angles

and the shared side.

50) Are the triangles congruent? If so, state theorem used.

Yes, by HL

32

x

9x - 7 4x + 8

6x + 2

51)Given: AD CD; BD bisects ADC

Prove: ΔABD ΔCBD

Statements Reasons S 1) Given A 2) ADB CDB Def. of angle bisect S 3) BD BD Reflexive

4) ΔABD ΔCBD SAS

52) Given: EH bisects DG , D G

Prove: ΔDEF ΔGHF

53) In DFE, FK is a median, FJ is an angle bisector, and HF is an altitude.

a) Name 2 right angles: DHF , EHF

b) Name 2 congruent (non-right) angles:

DFJ EFJ

c) Name 2 congruent segments: DK EK

Statements Reasons A 1) Given S 2) DF FG Def of bisect

A 3) DFE HFG Vertical angle thm 4) ΔDEF ΔGHF ASA

A

B

C

D

54) If R is the circumcenter of ABC, find the value of x, y, and z.

RC=RA=RB (circumcenter is same distance from each vertex) Circumcenter is POC of bisectors so line j

goes through the midpoint of CA 3 15 363 51

17

zz

z

4 8 364 28

7

xx

x

8 4 128 16

2

yy

y

55) C is the centroid of JLM (centroid is 2/3 distance from vertex to midpt) A) CZ = 3 Find JC and JZ

2( )

6 36

9JCJ CZ

JZ

C

B) MC = 8. Find CY and MY C) LX = 24. Find CX and CL

44 2

1

2

18

C

CY

C

MY

Y M

1

3

2( )8

16CXC

CX LX

CL X

56) Name all the angles whose measures are:

A) less than 8. 4, 6, 7, 2

B) greater than 2. 4, 8

P Q

R S

57) Name the angles from greatest to smallest.

Largest angle is across from longest side, smallest angle is across

from shortest side. , ,A C B

58) Determine the relationship between the given pair of angle or

segment measures. (use hinge theorem)

A) JM _>_ KL B) mCDA _<_ mDAB

59) If mS = 5x and mQ = 155, find the value of x for which PQRS must

be a parallelogram.

Opposite angles are congruent

5 15531

m S m Qx

x

60) In the parallelogram, find the value of x, AB, and BC.

Opposite sides are congruent

4 10 22 10

4(5) 102(5

104

5

6)

AB DCx x

xABB

x

C AD

61) For parallelogram ABCD, AC = 40, AG = 2x + 4, DG = 4y – 10,

GB = y + 5. Find x and y.

Diagonals bisect each other.

2( )40 2(2 4)40 43 4

8

82

AC AG

x

x

x

x

4 10 5

53 15

DG GBy y

yy

62) Find the sum of the interior angles of a convex 15-gon.

Sum of interior angles = (n-2)180

(15 2)180(13)1802340S

SS

A B

C D

4x – 10

2x

2x – 4

A B

C D G

63) Find the measure of an interior angle of a regular dodecagon.

( 2)180int

(12 2)180int

12

1800in

int 150

t12

n

n

OR

360 36030

12int 1int 30

80180 150

extn

ext

64) What do these symbols mean?

a. congruent

b. AB segment with endpoints of A and B

c. AB line through points A and B

d. AB ray with starting point at A and going through point B

e. A angle with vertex at A

f. m A measure of angle with vertex at A

g. perpendicular

h. ABC triangle with vertices A, B, and C

j. a//b line a parallel to line b