Geometry Honors District Midterm

| 137

b base

Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet

A area h height B area of base w width C circumference d diameter V volume r radius P perimeter

slant height of base

a apothem S.A. surface area

orV bwh V Bh

S A . . S A. .

orbh bw hw 2 2 2 Ph B2

orV r h ! 2 S A. . S A. .

rh r2 2 2! ! rh B2 2!

or

1 3

orV r h 1 3 1 3

! 2

1 2

S A. . r B( ) 1 2

2!

Sum of the measures of the interior angles of a polygon

Measure of an interior angle of a regular polygon

where: n represents the number of sides

180 2( )n

Geometry EOC Appendix G

Geometry EOC Test Item Specifications Florida Department of Education |

180 2( )n n

G-4

Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet

Slope formula

x2 x1

y2 y1

x1 y1 x2 y2

Slope-intercept form of a linear equation

Point-slope form of a linear equation x1 y1

x1 y1

Special Right Triangles

x x

x

x x

x

Distance between two points

− −(x2 x1)2 + (y2 y1)

2

Midpoint between two points

( (

Quadratic formula -

Trigonometric Ratios

Geometry EOC Appendix G

opposite

opposite

hypotenuse

hypotenuse adjacent

adjacent

sin A°

tan A°

cos A°A°

G-5 | Geometry EOC Test Item Specifications Florida Department of Education

1

Geometry Honors District Midterm Exam

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Which one of the following is NOT one of the undefined terms in geometry?

a. point c. plane

b. line d. space

____ 2. What is a valid explanation of how to construct JK so that JK ! FG?

a. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG . Put the compass point on G and draw

an arc that intersects the ray. Label JK. JK ! FG

b. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG . Put the compass point on J and draw an

arc that intersects the ray. Label the point of intersection K. JK ! FG

c. (1) Measure the segment FG. (2) Open your compass to the length of FG . Put the compass point on K and draw

an arc that intersects the ray. Label the point of intersection J. JK ! FG

d. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG . Put the compass point on J and draw an

arc that intersects the ray and is two times the length of FG. Label the point of intersection K.

JK ! FG

2

____ 3. R is the midpoint of PS. The coordinates of S and R are given below. What are the coordinates of P?

R: (5, 4) S: (6, 1)

a. (4, 7) b. (10, 8) c. (5.5, 2.5) d. (7, "2)

____ 4. An angle has a measure of 29.6°. What is the measure of the supplement of its complement?

a. 29.6° c. 90°

b. 60.4° d. 119.6°

____ 5. The circle shown below is centered at the origin and contains the point (-4, -2).

Which of the following is closest to the length of the circumference of the circle?

a. 4.47 c. 28.09

b. 8.94 d. 62.83

3

____ 6. The volume of a regular hexahedron is 216 units cubed. What is it’s surface area?

a. 36 units squared c. 108 units squared

b. 88.18 units squared d. 216 units squared

____ 7. If KM = MZ, then K is the midpoint of KZ.

a. True

b. False

____ 8. Draw a Venn diagram to illustrate this conditional statement:

If it is a car, then it is a motor vehicle.

a. c.

b. d.

4

____ 9. The converse of the inverse of a conditional statement has the same truth value as which of the following?

I. The original conditional statementII. The converse of the original conditional statementIII. The inverse of the original conditional statementIV. The contrapositive of the original conditional statement

a. I c. I and IV

b. III d. II and III

____ 10. Tien makes the following argument and reaches the conclusion below.

Given: If a number is divisible by 4, then the number is divisible by 2. 16 is divisible by 4.Conclusion: 16 is divisible by 2.

Which law guarantees Tien that she has drawn a valid conclusion?

a. Law of Syllogismb. Law of Detachmentc. Law of Inductive Reasoningd. Law of Conclusions

____ 11. What is the value of c such that the points "3, 5ÊËÁÁ

ˆ¯̃̃ and 8, cÊ

ËÁÁˆ¯̃̃ lie on a line with slope " 1

5?

a. 145

c. 3

b. 365

d. -50

____ 12. If AB # CD and XY# CD , then AB is ____________ parallel to XY .

a. always

b. sometimes

c. never

5

____ 13. Complete the following truth table and choose the one that is filled out correctly below.

p q r $ q r% $ q

T T T

T T F

T F

T F

F

F

F

F

a.

p q r $ q r% $ q

T T T F F

T T F F F

T F T T T

T F F T F

F T T F F

F T F F T

F F T T F

F F F T F

c.

p q r $ q r% $ q

T T T F F

T T F F F

T T T F F

T T F T F

F F T T T

F F F T F

F F T T T

F F F T F

b.

p q r $ q r% $ q

T T T F F

T T F F F

T F T T T

T F F T F

F T T F F

F T F F F

F F T T T

F F F T F

d.

p q r $ q r% $ q

T T T F F

T T F F F

T F T T T

T F F T F

F T T F F

F T F F F

F F T T F

F F F T F

6

____ 14. Sebastian was asked to write the equation of the line that contains the point "1, 2ÊËÁÁ

ˆ¯̃̃ and is parallel

to the line y"2=3 x"1( ) . Which equation below represents the line Sebastian is looking for in slope intercept form?

a. y = 3x + 2 c. y = 3x + 5

b. y = 13

x + 2 d. y = " 13

x + 5

____ 15. Complete the two-column proof.

Given: 11x " 6y = "1; x = 8

Prove: 896

= y

11x " 6y = "1; x = 8 a. ________

88 " 6y = "1 b. ________

"6y = "89 c. ________

y = 896

d. ________

896

= y e. ________

a. a. Givenb. Symmetric Property of Equalityc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

c. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

b. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Symmetric Property of Equality

d. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Commutative Property

7

____ 16. Identify the missing justifications used to find the value of x.

m&PQR = x + 7, m&SQR = x + 3, and m&PQS = 100.

m&PQR + m&SQR = m&PQS a. __________x + 7 + x + 3 = 100 b. Substitution Property

2x + 10 = 100 c. Simplify2x = 90 d. __________

x = 45 e . Division Property of Equality

a. Angle Addition Postulate; Division Property of Equality

b. Angle Addition Postulate; Subtraction Property of Equality

c. Protractor Postulate; Addition Property of Equality

d. Protractor Postulate; Subtraction Property of Equality

____ 17. Use the diagram below, where a || b.

Which pair are alternate exterior angles?

a. &3 and&4 c. &1 and&6

b. &1 and&2 d. &2 and&6

8

____ 18. What is m&UST?

a. 36° c. 104°

b. 76° d. 114°

____ 19. Michael is building a chair for his front porch. He cuts each leg so that they form a 52° angle with the base of the seat of the chair as shown in the diagram below.

What angle does the front of each leg make with the ground, x, in order to ensure that the seat of the chair is parallel with the ground?

a. 138° c. 52°

b. 128° d. 38°

____ 20. If DNP ! HKF, which of the following is NOT necessarily true?

a. NP ! KF c. &D ! &H

b. DP ! HF d. &P ! &K

9

____ 21. Which of the following is the construction of the segment that is perpendicular to AB through point C?

a. c.

b. d.

____ 22. Using the information below, what is the most accurate classification of 'PQR? How long is QR?

a. equilateral, QR = 24 c. acute, QR = 5.5

b. isosceles, QR = 18.5 d. equilateral, QR = 35

10

____ 23. 'MNP is an isosceles triangle with MN ! PN. The measure of &N is 3 times the measure of &P. What is the measure of &N?

a. 144° c. 36°

b. 108° d. 18°

____ 24. In the quadrilateral below, what is the sum of the degree measures of angles 1, 2, and 3?

a. 70° c. 290°

b. 110° d. 320°

____ 25. Find the values of x and y.

a. x = 90, y = 47 c. x = 47, y = 43

b. x = 43, y = 47 d. x = 90, y = 43

11

____ 26. Given: PQRS is a rectangle.Prove: PSR ! QRS

Which triangle congruence property is missing in step 5?

Statement Reason

1. PS ! QR 1. Opposite sides of a rectangle are congruent.

2. &PSR and &QRS are right angles. 2. All angles of a rectangle are right angles.3. SR ! RS 3. Reflexive Property of Congruence4. &PSR ! &QRS 4. All right angles are congruent.5. PSR ! QRS 5. ?

a. AAS c. SSS

b. ASA d. SAS

____ 27. To prove that parallelogram ABCD with vertices A(–5, –1), B(–9, 6), C(–1, 5), and D(3, –2) is a rhombus, you must show that it is a parallelogram with perpendicular diagonals. What are the slopes of the diagonals?

a. 32

and " 23

c. 12

and "2

b. 1 and "1 d. " 47

and 47

12

____ 28. What is the translation image of the triangle shown after a translation with the rule (x, y) ( (x " 3, y + 3)?

a. c.

b. d.

13

____ 29. If a triangle is partially formed by the vertices "2a, 0ÊËÁÁ

ˆ¯̃̃ and 2a, 0Ê

ËÁÁˆ¯̃̃, what is the number of unique

vertices for which the triangle formed is regular?

a. infinite c. 1

b. 2 d. 0

____ 30. An altitude of an equilateral triangle intersects the opposite side at the midpoint. Which of the following could be used to construct an altitude of an equilateral triangle?

a. copying an angle c. parallel line

b. copying a segment d. perpendicular bisector

____ 31. Where is the circumcenter of any given triangle?

a. the point of concurrency of the altitudes of the triangle

b. the point of concurrency of the perpendicular bisectors of the sides of the triangle

c. the point of concurrency of the bisectors of the angles of the triangle

d. the point of concurrency of the medians of the triangle

____ 32. In 'ACE, G is the centroid and BE = 9. Find BG and GE.

a. BG = 2 14

, GE = 6 34

c. BG = 6, GE = 3

b. BG = 3, GE = 6 d. BG = 4 12

, GE = 4 12

14

____ 33. Which inequality shows the possible lengths for the third side of the triangle below?

a. x > 9.8 c. 3.2 < x < 6.6

b. x < 3.4 d. 3.4 < x < 9.8

____ 34. What is the correct order of the sides of the triangle from longest to shortest?

a. LN, LM, MN c. LN, MN, LM

b. LM, MN, LN d. MN, LN, ML

____ 35. For an indirect proof of the statement below, what do you temporarily assume as the first step of the proof?

The two lines are parallel.

a. The two lines are NOT parallel.

b. The two lines are NOT rays or segments.

c. The two lines are the same.

d. The two lines are skew.

____ 36. The measure of an exterior angle of a regular polygon is 45°. What type of polygon is it?

a. dodecagon c. nonagon

b. decagon d. octagon

15

____ 37. Compare PR and QS.

a. PR = QS c. PR > QS

b. PR < QR d. PR < QS

____ 38. What is the value of x in parallelogram WXYZ?

a. 22 c. 12

b. 18 d. 8

____ 39. LM is the midsegment of trapezoid ABCD. AB = 46 and DC = 125. What is LM?

a. 171 c. 57

b. 85.5 d. 95.5

16

____ 40. For his mathematics assignment, Armando must determine the conditions that will make quadrilateral ABCD, shown below, a parallelogram.

Given that the m&DAB = 400 , which of the following statements will guarantee that ABCD is a parallelogram?

a. m&DCB = 40 0 ;m&ABC= 140 0

b. m&ADC+m&DCB +m&ABC+ 40 0 = 360 0

c. m&ABC+ 40 0 = 180 0

d. m&DCB = 40 0

Short Answer

41. What is the length of RT?

42. How many edges does a triangular prism have?

43. In a regular polygon, the sum of the interior angles is equal to twice the sum of the exterior angles. What is the measure of an interior angle of the polygon?

17

44. To the nearest tenth, what is the length, in units, of MN?

45. Assume all angles are right angles. What is the area of the figure?

46. What is the surface area of the shoebox with the dimensions shown below?

47. An aquarium has a giant fish tank in the shape of a cylinder.

To the nearest cubic foot, what is the volume of the fish tank? Use 3.14 for ).

18

48. In this drawing, line p is parallel to line j and line t is perpendicular to AB(**

.

What is the measure of &BAC?

49. Find the x-coordinate of the circumcenter of 'ABC with vertices A("2, 4), B("2, "2), and C(4, "2).

50. Find the value of x.

Geometry Honors Mid-Term Fill-In Response Answer Sheet Name: _________________________________ Date: _______ Period: ____

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

ID: A

1

Geometry Honors District Midterm ExamAnswer Section

MULTIPLE CHOICE

1. ANS: D STA: MA.912.G.8.1 2. ANS: B STA: MA.912.G.1.2 3. ANS: A STA: MA.912.G.1.1 4. ANS: D STA: MA.912.G.8.2 5. ANS: C STA: MA.912.G.1.1 6. ANS: D STA: MA.912.G.7.1 7. ANS: B STA: MA.912.G.8.4 8. ANS: A STA: MA.912.G.8.4 9. ANS: C STA: MA.912.G.8.4 10. ANS: B STA: MA.912.D.6.4 11. ANS: A STA: MA.912.A.3.9 12. ANS: B STA: MA.912.D.6.4 13. ANS: B STA: MA.912.D.6.1 14. ANS: C STA: MA.912.A.3.10 15. ANS: B STA: MA.912.D.6.4| MA.912.G.8.5 16. ANS: B STA: MA.912.D.6.4| MA.912.G.8.5 17. ANS: D STA: MA.912.G.1.3 18. ANS: C STA: MA.912.G.1.3 19. ANS: B STA: MA.912.G.1.3 20. ANS: D STA: MA.912.G.4.6 21. ANS: D STA: MA.912.G.1.2 22. ANS: A STA: MA.912.G.4.1 23. ANS: B STA: MA.912.G.4.1 24. ANS: C STA: MA.912.G.2.2 25. ANS: D STA: MA.912.G.4.1 26. ANS: D STA: MA.912.D.6.4 | MA.912.G.4.6 | MA.912.G.8.5 27. ANS: A STA: MA.912.G.3.3 28. ANS: C STA: MA.912.G.2.4 29. ANS: B STA: MA.912.G.4.8 30. ANS: D STA: MA.912.G.4.2 31. ANS: B STA: MA.912.G.4.2 32. ANS: B STA: MA.912.G.4.2 33. ANS: D STA: MA.912.G.4.7 34. ANS: C STA: MA.912.G.4.7 35. ANS: A STA: MA.912.D.6.4 36. ANS: D STA: MA.912.G.2.2 37. ANS: C STA: MA.912.G.4.7 38. ANS: B STA: MA.912.G.3.1 39. ANS: B STA: MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4

ID: A

2

40. ANS: A STA: MA.912.G.8.4

SHORT ANSWER

41. ANS: 40

STA: MA.912.G.1.1 42. ANS:

9

STA: MA.912.G.7.1 43. ANS:

120°

STA: MA.912.G.2.2 44. ANS:

6.7

STA: MA.912.G.1.1 45. ANS:

360 square meters

STA: MA.912.G.2.5 46. ANS:

256 square inches

STA: MA.912.G.7.5 47. ANS:

196 ft3

STA: MA.912.G.7.5 48. ANS:

37°

STA: MA.912.G.1.3 49. ANS:

1

STA: MA.912.G.4.2 50. ANS:

63

STA: MA.912.G.2.2