GEOMETRY SEMESTER EXAM-CHAPTERS 1-6 · Web viewSmart’s Mill Middle School Geometry Semester Exam...

Smart’s Mill Middle School

Geometry Semester Exam Review

2014 – 2015

You must show your work to receive credit!

Mrs. CoxA note to remember, for this review AND the actual exam: It is always helpful to draw a picture.

I encourage you to do that for any problem a picture is not given. GOOD LUCK.

Name:___________________

Date:_______________

Period: _____

DUE: Monday, January 12th – 1st and 2nd blocksDue: Tuesday, January 13th – 6th and 7th blocks

Collected – and one problem on each page graded for accuracy. So you will get a combined grade for

completeness and accuracy – late -5 points! Geometry Semester Exam Review 1

Part I. Fill in the blank.

1. A line segment contains ______________________________________________________.

2. If AM = MB and points A, M and B are collinear, then ____________________________________________.

3. In a triangle, the smallest angle is (where?) _____________________________________________________ .

4. If two parallel lines are cut by a transversal, all corresponding angles are ___________.

5. If A is between B and C and are collinear, then _______________________________ .

6. A right triangle has (what types of angels?)__________________________ and _______________________ .

7. _____, _____, _____, _____, _____ (5) are methods to prove triangles congruent.

8. The intersection of two planes is a ____________________.

9. In quadrant ___________, the x and y coordinates are both negative.

10. Acute angles measure _____________________________________.

11. Equiangular triangles are also ____________________________.

12. Parallel lines have the same _________________.

13. The intersection of two lines is a ___________________________.

14. If two angles are supplements of congruent angles, then the two angles are ___________.

15. Corresponding sides of congruent triangles are __________________________.

16. Skew lines are __________________________ and ___________________________ .

17. The slope of a horizontal line is _____________ .

18. Two angles are complementary if ________________________________________________________ .

19. The angles in a triangle sum to _______________ .

20. Vertical angles are ____________.

21. An isosceles triangle has _________________ and ______________________________________________ .

22. An equilateral triangle has ____________________ and _________________________________________.

23. If a conditional statement is false, then so is its _____________________________________ .

24. The hypotenuse of a right triangle is opposite the ________________________________________________.

25. If two sides of a triangle have length 4and 6 then the third side must be __________________________.

26. A(n) _____________________ of a right triangle is the longest side.

27. The slope of a vertical line is _____________________ .

28. In a triangle, the largest angle is ______________________________________________________.

29. Two lines that are not parallel or skew are _____________________.

30. The three medians of a triangle intersect ____________________________ and _______________________.

31. When two parallel lines are cut by a transversal, the exterior angles are ______________or _______________.

32. If two lines are parallel, then alternate interior angles are __________________.

Geometry Semester Exam Review 2

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Part II. Free response by chapter.

True or false. Chapter 1

1. Points A, B and H are collinear. _____ 4. Points E, J and F are collinear. _____2. Point A lies on line m. _____ 5. Point C lines on line l. ______3. Points B, C and H are coplanar. _____ 6. Plane ABC and plane BCF intersect at point B. _____

For questions 7 – 11, refer to the diagram at the right.

7. Name the intersection of C⃗D and plane P. _____________

8. If T⃗B and T⃗C were drawn, what would be their intersection? ______

9. Name the intersection of line l and C⃗D . ______________10. Name four noncoplanar points. _____________________11. Write another name for plane P. ____________________

For questions 12, write the following using symbols. Do not draw.12. a. perpendicular ________ d. parallel ________ g. ray KL ________

a. line segment AB ________ e. the length of line segment CD ________b. angle EFG ________ f. the measure of angle HIJ _____________

13. Find the length of the segment with endpoints H(2, 3) and J(6, 7). ____________________

14. Find the midpoint of the segment MN with endpoints M(8, 9) and N(-2, 1). ________________

For questions 15 – 17, determine whether each statement is true of false.15. If B is between M and T, MB = BT – MT. ________

16. If C is the midpoint of , then CT = TA. ________17. Every segment has only one bisector. _______

18. If , find . _______

19. Find m∠ ABC if BD bisects ___________

For questions 20 – 23, refer to the figure at the right.20. Name two right angles. __________ ___________21. Name two supplementary angles. . __________ ___________22. Name two congruent angles that are not right angles. . _____ ______23. Name the obtuse angle. . __________

24. The measure of an angle is three times the measure of its supplement. Find the measure of the angle. _____

25. Find the value of y. ________

26. Find if and ___________________

27. Find the value of x if , and ____________Geometry Semester Exam Review 3

Chapter 2For questions 1 - 3, determine if the conclusion is true or false based on the given information.1. Given: and are adjacent angles.

B⃗C and B⃗A are opposite rays. _________________________________Conjecture: and are supplements.

2. Given: PQ⊥PR . Conjecture: is a right angle. _________________________________

3. Given: J, K and L are collinear. Conjecture: JK + KL = JL. _________________________________

For questions 4 - 6, write the statement in if-then form. Underline the hypothesis once, conclusion twice.4. Two lines intersect exactly one point. _____________________________________________________________

5. All tigers are cats. _____________________________________________________________________________

6. All right angles measure 90 degrees. ______________________________________________________________

Write the converse, inverse and contrapositive of the conditional statement.7. Vertical angles are congruent. ___________________________________________________________________

Converse:______________________________________________________________________________Inverse:________________________________________________________________________________Contrapositive:__________________________________________________________________________

Complete the following statements.8. A plane contains _______________________________________________________________________.9. A line contains _______________________________________________________________________.

If possible, write the conclusion. State the law of logic that you used, or write “no conclusion”.10. a) If you have a driver’s license, then you may drive a car.

b) Cindy has a driver’s license.c)__________________________________________________________________________________________

11. a) If , then .

b) If , then CD = AB.c)_________________________________________________________________________________________

12. a) All right angles are congruent.b) Vertical angles are congruent.c)_________________________________________________________________________________________

For questions 13 – 15, name the property of equality that justifies each statement.13. If and , then . _________________________________________14. If AB = CD, then CD = AB. ___________________________________________________________

15. If , then .____________________________________________________________16. In the conditional “If p, then q”, the q is called the _____________________.

Geometry Semester Exam Review 3x+65x-18

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17. Find the measure of . _____________________Chapter 3

1. Name a pair of skew lines. _________________

Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special anglepair name.

2. and __________________________3. and __________________________4. and _________________________5. and __________________________6. and __________________________7. If , , and l||m , find the angle measures. _____.

_____, _____, _____, _____, _____, _____, _____, _____,

Find the value of x and y.8. l||m ________ _________ 9.

________ ________

Find the value of x so that p||q .10. ________ 11. ________

12. Tell whether a line whose slope is undefined is horizontal, vertical or neither. _______________________

13. Find the slope of the line passing through (-3, 0) and (2, -1). __________________

14. Find the slope of a line parallel to the line passing through (5, -3) and (8, 2). __________________

15. Find the slope of the line perpendicular to the line passing through (4, -3) and (1, -1). ____________________

16. Write the equation of the line with a slope of 4 passing through (-1, 3). _________________

17. Write the equation of the line parallel to passing through (-2, 3). ______________


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18. Write the equation of the line perpendicular to passing through (1, 4). _____________

Chapter 4Determine whether each statement is true or false.

1. All isosceles triangles are acute. ____________2. An acute triangle can be equilateral. ___________3. A scalene triangle is never obtuse. __________4. A right triangle can be isosceles. __________

Use the given conditions to classify each triangle by its sides and by its angles.5. ΔWHO , with WH = WO = 5 cm. ______________ ______________6. Δ BAG , with GB = 4 cm , BA = 3 cm. _______________ ______________

Find the value of x.7. ______________

________________ 8.

Write a congruence statement for the congruent triangles in each diagram.

9. _____________________ 10. _______________________

Determine which postulate or theorem can be used to prove the triangles congruent.

11. _______ 12. _________ 13. ________

Always, sometimes or never.13. An equilateral triangle is _______________ an isosceles triangle.14. An isosceles triangle is __________ an equilateral triangle.15. A triangle __________ has one obtuse angle and one right angle.16. An equilateral triangle is _______________ an obtuse triangle.17. An equilateral triangle is _______________ an acute triangle.

Find the value of x and y.18. _____ _____ 19. _____ _____ 20. _____ _____


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21. What is the vertex for ___________Chapter 5

1. Name the triangle for which is a median. _________

2. Name an altitude of Δ AGC . ______

3. Name a median to in Δ AGC . _______

4. Name a perpendicular bisector ______ to triangle _____.

5. Name an angle bisector. _______ to angle _____ .

List the sides of ΔWXY in order from longest to shortest if the angles of ΔWXY have the indicated measures.

6. 4x – 1 7x + 3 3x – 4 _____ _____ _____

7. 5x + 2 6x - 5 48 – 2x _____ _____ _____

8. Two sides of a triangle are 16 and 22 centimeters in length. Determine whether 39 centimeters can be the length of the third side? _________

9. Two sides of a triangle are 21 and 24 centimeters in length. Determine whether 40 centimeters can be the length of the third side? _________

Write the inequality relating each pair of measures.10. 11.

Write an inequality to describe the possible values of x.

12. _____________ 13. __________


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Part III: Multiple ChoiceChoose the best answer for each question.

Chapter 11. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).

A. 13 B. 17 C. 5 D. 12

2. Points A, B and D A. determine a plane B. are collinearC. are contained in only plane P D. are noncoplanar points

3. What is the intersection of planes P and R.

A points A, D and B B. A⃗B C. D.

4. What is the measure of if R is between Q and T, QR = 14 and RT = 5?A. 10 B. 11 C. 19 D. 9

5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).A. (3, 4) B. (2, 4) C. (4, 8) D. (1, -1)

6. What are the sides of ?

A. W⃗B and W⃗F B. A⃗B and W⃗F

C. W⃗B and W⃗G D. W⃗F and W⃗G

7. and are A. adjacent B. vertical C. supplementary D. complementary

8. and are A. adjacent B. vertical C. supplementary D. complementary

9. and are A. adjacent B. vertical C. complementary D. linear pair

10. and are A. adjacent B. vertical C. linear pair D. complementary

11. Find .A. 25 B. 155C. 175 D. 5

12. If and , find A. 150B. 130C. 70 D. 80


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13. Find if S⃗T bisects , and A. 48 B. 18C. 9 D. 24

Chapter 21. Choose the converse of “If , then = .

A. If = , then B. If , then C. If = , then = .D. None of these

2. Identify the hypothesis of the statement “If today is Tuesday, then tomorrow is Wednesday.”A. Today is not TuesdayB. Today is WednesdayC. Today is TuesdayD. Tomorrow is Wednesday

3. Identify the if-then form of the following: All cars have four wheels.A. If a vehicle has four wheels, then it is a car.B. If a vehicle is a car, then it has four wheels.C. If a vehicle is not a car, then it does not have four wheels.D. None of these

4. Choose the statement that follows (1) and (2) by the law of detachment.(1) Right angles are congruent.(2) and are right angles

A. m = 90 B. m = 90 C. D. =

5. Which statement represents the law of syllogism.A. If is a true conditional and p is true, then q is true.B. If and are true conditionals, then is true.C. If a, b and c are real numbers, then a(b + c) = ab + ac.D. None of these

6. The transitive property of equality states “If a = b and b = c, then _____”.A. b = a B. a = c C. c = b D. b = b


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7. and form a linear pair and Find A. 62 B. 28 C. 118 D. 90

Chapter 3

1. Given l||m and = 72, find .A. 108 B. 72C. 18 D. 112

2. Given l||m , = 9x +5 and = x + 37, find the value of x.A. 32 B. 4C. 41 D. 39

3. Given and = 3x + 28, find the value of x so that l||m .A. 26 B. 13C. 67 D. 75

Chapter 4

1. A right triangle must be A. isosceles B. acute C. scalene D. either isosceles or scalene

2. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5.A. 39 B. 13 C. 12 D. 4

3. In Δ ABC , what is the angle opposite ?

A. B. C. D.

4. In Δ DEF , if and is the hypotenuse, then Δ DEF isA. acute and scalene B. right and scaleneC. right and isosceles D. obtuse and isosceles

5. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?A. 85 B. 95 C. 133 D. 142

6. If Δ IGH≃Δ KLJ , then is congruent to A. B. C. D.

7. Which of the following is not a postulate used to prove the congruence of two triangles?A. ASA B. SSA C. SAS D. SSS

8. The measure of the vertex angle of an isosceles triangle is 120. That is the measure of the base angle?A. 60 B. 30 C. 35 D. 40


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9. Name one additional pair of corresponding parts that need to be congruent in order to prove that Δ STP≃Δ MKO by ASA.

A. B.

C. D.

Chapter 51. Identify the median of Δ ABC .

A. B.

C. D. G⃗H

2. Identify the altitude of Δ ABC .

A. B

C. D. G⃗H

3. In Δ ABC , if and is an angle bisector, find A. 90 B. 51C. 39 D. 12

4. What is the longest side of the figure QUAD.

A. B

C. D.

5. In Δ EFG , = 6x – 8, 7x + 3, and = 3x – 7. Choose the list that shows the sides correctly ordered from shortest to longest.

A. B.

C. D.

6. Determine which set of numbers can be the measures of the sides of a triangle.A. 13, 10, 16 B. 1, 2, 3 C. 5.2, 11, 4.9 D. 208, 9, 219

7. Two sides of a triangle have lengths 15 cm and 19 cm. Which measurement can be the length of the third side?A. 6 cm B. 4 cm C. 40 cm D. 36 cm

8. If the sides of a triangle have measures 3x + 4, 6x – 1 and 8x + 2, find all possible values of x.

A. x > -1 B. C. D. x > 0Geometry Semester Exam Review 11

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9. If M is the midpoint of , , JL = 10x + 2, and LK = 6x + 14, which is a possible value of x?A. 1B. 2C. 3D. 4

Properties

State the property, theorem, postulate or definition used to make the conclusion.

1. If UV = VW, then VW = UV. ___________________________________________________

2. If is a right angle, then is 90 . _____________________________________________

3. 2(x – 50) = 2x – 100. __________________________________________

4. If and are vertical angles, then . ______________________ ___________________

5. If , then is a right angle. _________________________

6. AB + BC = AC. __________________________________________

7. If , then . ______________________________________________________

8. . ________________________________________________________________________

9. If 2x + 4 = 17, then 2x = 13. ____________________________________________________________

10. T is the midpoint of , then . ________________________________________________

11. If and , then . ________________________________________________

12. If and are a linear pair, then they are supplementary. _______________________________

13. If A⃗B bisects , then . ___________________________________________

14. If and are supplementary, then . _____________________________________

15. If l||m , then . _______________________________________________________

16. , then l||m . _____________________________________________________________


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Proofs

1. Given: Prove: Δ AFR≃ΔTFR

F is a midpoint of

Statements Reasons1. 1. Given

2. ___________________________ 2._______________________________________________________

3. ___________________________ 3._______________________________________________________

4. F is a midpoint of 4. Given

5. ___________________________ 5._______________________________________________________

6. ___________________________ 6. ______________________________________________________

7. ____________________________ 7.________________________________________________________

2. Given: W is a midpoint of Prove: ZV||YX

Statements Reasons

1. ___________________________ 1. ______________________________________________________

2. ___________________________ 2. ______________________________________________________

3. ___________________________ 3. ______________________________________________________

4. ___________________________ 4. ______________________________________________________

5. ___________________________ 5. ______________________________________________________


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6. ___________________________ 6. ______________________________________________________

7. ____________________________ 7._______________________________________________________

3. Given: EA||DC Prove:

Statements Reasons

1. 1. Given

2. EA||DC 2. Given

3. ____________________________ 3. _____________________________________________________

4. ____________________________ 4. ______________________________________________________

5. __________________________ 5. _____________________________________________________

4. Given: a||b1 4

Prove: c||d

Statements Reasons

1. a||b 1. Given

2. 1 3 2.__________________________________

3. 3 1 3.__________________________________

4. 1 4 4. GivenGeometry Semester Exam Review 14

5. 3 4 5.__________________________________

6. c||d 6.__________________________________


GEOMETRY SEMESTER EXAM-CHAPTERS 1-6 · Web viewSmart’s Mill Middle School Geometry Semester Exam...

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